Question

Find the value of x in the isosceles triangle shown

Answer 1

x = 8√5

Explanation:

The large triangle is divided into two smaller ones. The right one has one leg of length 8, one leg of length x/2, and hypotenuse of length √80.

Appling the Pythagorean Theorem, we can find x:

8² + (x/2)² = (√80)²,

or: x^2

64 + x^2/4 = 80, or ------- = 80

4

Then x^2 = 320 = 64*5. Taking the square root of both sides, we get:

x = 8√5