Question

*The length of the congruent sides of an isosceles triangle is 17cm. If the base of the triangle is 16 cm, find the length of the median.*

1️⃣ 18 cm
2️⃣ 8 cm
3️⃣ 15 cm
4️⃣ 8.5 cm​

Answer 1

The median is 15cm.

Explanation:

Given that the The length of the congruent sides of an isosceles triangle is 17cm . the base of the triangle is 16 cm . And we need to find the median .

We know that in a isosceles triangle

• All perpendicular bisector , altitude and median concide with each other.

This means that the base will be divided into two equal parts For Figure refer to attachment .

Using Pythagoras Theorem :-

⇒ BM² + AM² = AB²

⇒ (17cm)² = (8cm)² + AM²

⇒ 289 cm² = 64cm² + AM²

⇒ AM² = 289 cm² - 64 cm²

⇒ AM² = 225 cm²

⇒ AM = √225 cm²

⇒ AM = 15 cm .

Hence the measure of median is 15 cm .