Question

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

Answer 1

B

Explanation:

Since the triangle is isosceles, then the segment from the vertex is a perpendicular bisector and the triangle is divided into 2 right angles with legs 12 and
`(1)/(2)` x with hypotenuse 15

Using Pythagoras' identity in the right triangle

(
`(1)/(2)` x )² + 12² = 15²

`(1)/(4)` x² + 144 = 225 ( subtract 144 from both sides )

`(1)/(4)` x² = 81 ( multiply both sides by 4 to clear the fraction )

x² = 324 ( take the square root of both sides )

x =
`√(324)` = 18 → B