Question

Find the value of x in the isosceles triangle show below.

Answer 1

x = 8

Explanation:

Since the triangle is isosceles then the segment from the vertex is a perpendicular bisector, dividing the triangle into 2 right triangles.

Using Pythagoras' identity on the right triangle on the left

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(
`(1)/(2)` x )² + 8² = (
`√(80)`)²

`(1)/(4)` x² + 64 = 80 ( subtract 64 from both sides )

`(1)/(4)` x² = 16 ( multiply both sides by 4 )

x² = 64 ( take the square root of both sides )

x =
`√(64)` = 8 ← positive value only required