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.
- A5
- B6
- C6.5
- D7
Solution & Step-by-step Explanation
The given sides of the triangle are a=5 cm, b=12 cm, and c=13 cm.
First, we observe that these sides form a Pythagorean triplet because:
5
2
+12
2
=25+144=169=13
2
Thus, the triangle is a right-angled triangle, where the hypotenuse is the longest side, which is 13 cm (side AC).
In any right-angled triangle, the length of the median drawn to the hypotenuse is exactly equal to half the length of the hypotenuse (since the circumcenter of a right-angled triangle lies at the midpoint of the hypotenuse).
Length of median=
2
Hypotenuse
=
2
13
=6.5 cm
First, we observe that these sides form a Pythagorean triplet because:
5
2
+12
2
=25+144=169=13
2
Thus, the triangle is a right-angled triangle, where the hypotenuse is the longest side, which is 13 cm (side AC).
In any right-angled triangle, the length of the median drawn to the hypotenuse is exactly equal to half the length of the hypotenuse (since the circumcenter of a right-angled triangle lies at the midpoint of the hypotenuse).
Length of median=
2
Hypotenuse
=
2
13
=6.5 cm