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Triangles Questions

Practice 67 Triangles questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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Total Questions
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5
Easy
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62
Medium
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Practice by Exam:Quantitative Aptitude(48)Mathematics(6)Geometry(5)Mental Ability and Reasoning(2)General Intelligence & Reasoning(1)General Intelligence and Reasoning(1)General Aptitude(1)Mathematics and Science(1)

About Triangles — practice questions, PYQs & concepts

Triangles is a frequently-tested topic on Quantitative Aptitude, Mathematics, Geometry. ExamTest.live currently lists 67 Triangles questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Triangles weight in competitive exams

Across our Triangles question bank, the largest sources are Quantitative Aptitude (48), Mathematics (6), Geometry (5), Mental Ability and Reasoning (2) and General Intelligence & Reasoning (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 5 easy Triangles questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Triangles Questions(1–67 of 67)

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Q1easymcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
The internal angle bisectors BI and CI of ∠B and ∠C of a ΔABC meet at point I. If ∠A=38
∘
, then what is ∠BIC equal to?
Q2mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
The lengths of the three sides of a triangle are given as 3cm, 4cm and 5cm. The ratio of their corresponding altitudes to the opposite vertices will be:
Q3mediummcqQuantitative AptitudeCompetitive Exam 20262026
33% accuracy
△XYZ is an isosceles triangle such that XY=XZ. It is given that YS⊥XZ and ZT⊥XY. What is the relation between YS and ZT?
Q4mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
The sides of a right-angled triangle, right-angled at B, are 6, 8 and 10 units. C is the vertex opposite to the side with length 8 units. What is the value of tan
2
A+cos
2
C?
Q5easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
△PQR and △ABC are two congruent triangles. If the area of △PQR is 225cm
2
, then the area of △ABC is:
Q6mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If three angles of a triangle are (18x+6
∘
), (10x+30
∘
) and (15x+15
∘
), then the triangle is:
Q7easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
In an isosceles △LMN, LM=LN, and ∠MLN=37
∘
. Find ∠MNL.
Q8mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
In , is a point on such that and is parallel to (where lies on ). If and are perpendicular to and , then what is the length of (in )?
Q9mediummcqMathematicsStaff Selection Commission2026
0% accuracy
In △DEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 1:3 and HF is 7.2cm, find the length of DF.
Q10mediummcqGeometryCompetitive Exam2026
0% accuracy
If O is the orthocentre of a ΔABC and ∠BOC=140
∘
, then the measure of ∠BAC is:
Q11mediummcqGeometryCompetitive Exam2026
0% accuracy
In a ΔABC, a line DE is drawn from D point on AB to E point on AC such that DE∥BC. Also AD:DB is 2:5. If AC is 4.2cm, then what is the length of AE?
Q12mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
In , and are points on the sides and , respectively, such that is similar to . If , then find .
Q13mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If is the mid-point of the side of , and the area of is , then the area of is:
Q14mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the side of an equilateral triangle is equal to , calculate the length (in ) of , where is the centroid of the triangle.
Q15mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If a triangle has its orthocenter and centroid at the same point, then which of the following is TRUE about the triangle?
Q16mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
In , , , and the bisectors of and meet at . Find .
Q17mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
and are on a common base , with and . Which of the following options is true?

image
Q18mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
In , is the internal bisector of , which meets side at . If and , then what is the ratio ?
Q19mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the length of the three sides of a triangle is 5 cm, 12 cm and 13 cm respectively, then calculate the length (in cm) of the median of side AC of the given triangle.
Q20mediummcqGeometrySSC CGL2026
0% accuracy
In △ABC, the median AD is 6 cm and CB is 12 cm, measure of angle CAB is _________.
Q21mediummcqMathematicsAIEEE 20072026
0% accuracy
Let , and be the vertices of a right angled triangle with as its hypotenuse. If the area of the triangle is , then the set of values which can take is given by:
Q22mediummcqQuantitative Aptitude@NUM: 63SSC CGL2026
0% accuracy
In , and are points on side and respectively. is parallel to . If divides in the ratio and length of is , what is the length of ?
Q23mediummcqGeometryCompetitive Exams2026
Two poles of heights and stand vertically on a plane ground. If the distance between their feet is , what is the distance between their tops?
Q24mediummcqQuantitative AptitudeSSC CGL2026
If the circumradius of an equilateral triangle is 12cm, then what is the value of the inradius (in cm) of the triangle?
Q25mediummcqQuantitative AptitudeSSC CGL2026
If the side of an equilateral triangle is 6
3

​
cm, then what is the length (in cm) of the circumradius of that triangle?
Q26mediummcqQuantitative AptitudeStaff Selection Commission2026
Consider two similar triangles and where vertices correspond precisely as , , and . Choose which of the following equations correctly represents the similarity of both triangles?

image
Q27mediummcqQuantitative AptitudeStaff Selection Commission2026
In an isosceles triangle, the angle bisectors of ∠B and ∠C intersect at point O. Find the angle ∠BOC (in degrees), when ∠ABC=∠ACB=75

image

∘
.
Q28mediummcqQuantitative AptitudeSSC CGL2026
In an isosceles triangle ABC, the angle bisectors of ∠B and ∠C intersect at point O. Find the angle ∠BOC (in degrees), when ∠ABC=∠ACB=75
∘

image

.
Q29mediummcqQuantitative AptitudeCompetitive Exam2026
In , the measure of angle is . If and , then what is the length (in ) of side ?
Q30mediummcqQuantitative AptitudeSSC CGL2026
Points P and Q lie on sides AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of areas of ΔAPQ:ΔABC is 25:36, then the ratio of AP:PB is:
Q31mediummcqQuantitative AptitudeSSC CGL2026
What is the altitude of an equilateral triangle whose side is 15cm?
Q32mediummcqQuantitative AptitudeCompetitive Exam2026
The length of a radius of a circle is and the length of a chord of the circle is , the distance of the chord from the center of the circle is
Q33mediummcqGeometryCompetitive Exams2026
A parallelogram, a rectangle and a triangular region stand on the same base and between the same parallels. If their areas are , and respectively, then
Q34mediummcqMental Ability and ReasoningUP Police Assistant Operator Exam2026
Find out the number of triangles in the given standard structural star or network diagram template having 28 constituent patterns.

image
Q35mediummcqQuantitative AptitudeCompetitive Exam2026
In a triangle , points , , and are the midpoints of the sides , , and respectively. If the area of the triangle is , then the area of the triangle is:
Q36mediummcqQuantitative AptitudeCompetitive Exam2026
In a right-angled triangle , , , and . The radius of the inscribed circle is:
Q37mediummcqQuantitative AptitudeCompetitive Exam2026
In a right-angled triangle , , , and . The radius of the inscribed circle is:

image
Q38mediummcqMathematicsCompetitive Exam2026
The areas of two similar triangles are and respectively. If the median of the smaller triangle is then the corresponding median of the larger triangle is
Q39mediummcqQuantitative AptitudeGeneral Aptitude Test2026
Two angles of a triangle are and . What is the value of the third angle in circular measure? (As per convention, do not use the symbol of radian.)
Q40mediummcqLogical Reasoningimage_146f63.png2026
How many triangles are there in the figure corresponding to Q.80 in image_146f63.png?

image
Q41mediummcqQuantitative AptitudeCompetitive Exam2026
If the median drawn on the base of a triangle is half its base, the triangle will be:
Q42mediummcqQuantitative AptitudeWBCS Prelims2026
The angle between the external bisectors of two angles of a triangle is , then the third angle of the triangle is
Q43mediummcqQuantitative AptitudeCompetitive Examination2026
In , , . If , then the value of (denoted here as for the targeted angle) is:
Q44easymcqQuantitative AptitudeSSC CGL2026
In △ABC, D is the mid-point of BC and G is the centroid. If GD = 10 cm, then the length of AD is ____________.
Q45mediummcqMathematicsAIEEE2026
If a vertex of a triangle is and the mid-points of two sides through this vertex are and , then the centroid of the triangle is:
Q46mediummcqMathematicsJEE Main2026
The -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as , and is:
Q47mediummcqGeneral Intelligence & ReasoningUP Police Constable Re-Exam2026
Count the number of triangles in the given figure.

image
Q48mediummcqGeneral Intelligence and ReasoningAdda2472026
Find out the number of triangles in the given figure.

image
Q49mediummcqQuantitative AptitudeCompetitive Exam2026
In △ABC, AB=9cm and AC=13cm, then the length of BC could be:
Q50mediummcqQuantitative AptitudeCompetitive Exam2026
In △ABC and △PQR, we are given ∠A=∠P and AC=PR.
Which of the following options needs to be satisfied for △PQR and △ABC to be congruent?

image
Q51mediummcqQuantitative AptitudePrepp2026
In , is the internal bisector of , meeting the side at . If and , then the ratio is:
Q52mediummcqQuantitative AptitudePrepp2026
Two circles with centers and have radii and , respectively. is tangent to both circles. If and intersect at the point , and , then find the value of (in ).
Q53mediummcqQuantitative AptitudePrepp2026
If is the mid-point of the side of , and the area of is , then the area (in ) of is:
Q54mediummcqQuantitative AptitudeSSC CGL2026
In a triangle ABC, P is the midpoint of BC. If AB = (2x+4) cm, AC = 6 cm and AP ⊥ BC, then the value of x is:
Q55mediummcqQuantitative AptitudeCompetitive Exam2026
If and , then both triangles and are similar by which of the following criteria?
Q56mediummcqQuantitative AptitudeCompetitive Exam Practice2026
The median AD of a triangle ABC is produced and a perpendicular CF is dropped on it. BE is perpendicular to AD. If BC=34cm and DF=8cm, what is the length (in cm) of BE?
Q57mediummcqQuantitative AptitudePractice Test2026
Read the question and statements provided and decide whether the data provided in the statements are sufficient to answer the question.
Question: Find the area of a triangle.
Statements:
I. One of its sides is .
II. It is an equilateral triangle.
Q58mediummcqQuantitative AptitudePractice Test2026
A question along with a set of statements is given. Find which of the given statements is/are sufficient to answer the question.
Question: Find the perimeter of a triangle given that:
Statements:
I. Area of the triangle is .
II. Height of the triangle is .
Q59mediummcqQuantitative AptitudeSSC CGL2026
In , at . is a point on such that . If and , then the value of is:
Q60mediummcqQuantitative AptitudeSSC CGL2026
In , is the bisector of and intersects at . If , and , then is equal to:
Q61mediummcqMental Ability and ReasoningUP Police Assistant Operator Exam2026
Find the number of triangles in the given standard multi-segmented triangular figure template containing a total of 12 triangles.

image
Q62mediummcqQuantitative AptitudePractice Test2026
In ΔABC, D and F are the midpoints of the sides AB and AC, respectively. E is a point on the segment DF such that DE:EF=1:2. If DE=4cm, then BC is equal to:
Q63mediummcqQuantitative AptitudeCompetitive Exam2026
In triangle , the length of side is less than twice the length of side by . The length of side exceeds the length of side by . If the perimeter is , find the length of the smallest side of the triangle .
Q64mediummcqQuantitative AptitudeCompetitive Exam2026
In a triangle PQR, RS intersects PQ at point S. The sides of the triangle QR=36cm, SQ=27cm, RS=18cm and ∠QRS=∠QPR. What is the ratio of the perimeter of △PRS to that of △QSR?
Q65easymcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2018
In the given figure and , then is equal to
Q66mediummcqMathematicsAIEEE 20042004
0% accuracy
The sides of a triangle are and for some Then the greatest angle of the triangle is
Q67mediummcqGeneral AptitudeGeneral Aptitude
8% accuracy
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PQR to the area of the trapezium SQRT?(Note: Assume the text asks for the ratio of Area of PQR to Area of SQRT based on the mathematical constraints provided)

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