Question

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

Answer 1

Answer:

B

Step-by-step 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 $\frac{1}{2}$ x with hypotenuse 15

Using Pythagoras' identity in the right triangle

( $\frac{1}{2}$ x )² + 12² = 15²

$\frac{1}{4}$ x² + 144 = 225 ( subtract 144 from both sides )

$\frac{1}{4}$ x² = 81 ( multiply both sides by 4 to clear the fraction )

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

x = $\sqrt{324}$ = 18 → B