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A question along with a set of statements is given below. We have to find which of the given statements is/are sufficient to answer the given question.

Question : Find the area of the triangle PQR.
Statements :
I. PQ = 5 m., PR = 5 m.
II. Length of PO is 4 m.

  1. A
    Both Statement I and Statement II together are sufficient.
  2. B
    Statement I alone is sufficient.
  3. C
    Statement II alone is sufficient.
  4. D
    Both Statement I and Statement II together also are not sufficient.

Solution & Step-by-step Explanation

* From Statement I, we only know that two sides of are equal (), making it an isosceles triangle. Without knowing the third side or any angle, the area cannot be calculated. Thus, Statement I alone is insufficient.
* From Statement II, the length of is given as . However, the position or nature of point is completely undefined (it is not stated whether lies on , or if is an altitude, median, etc.). Thus, Statement II alone is insufficient.
* Even combining both statements, since the exact relationship and orientation of point relative to the triangle is unknown, the area cannot be computed.

Therefore, both statements together are not sufficient.

Practice this question

Try it yourself before checking the explanation above.

image
A question along with a set of statements is given below. We have to find which of the given statements is/are sufficient to answer the given question.

Question : Find the area of the triangle PQR.
Statements :
I. PQ = 5 m., PR = 5 m.
II. Length of PO is 4 m.
A
Both Statement I and Statement II together are sufficient.
B
Statement I alone is sufficient.
C
Statement II alone is sufficient.
D
Both Statement I and Statement II together also are not sufficient.

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