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 [tex]\frac{1}{2}[/tex] x with hypotenuse 15
Using Pythagoras' identity in the right triangle
( [tex]\frac{1}{2}[/tex] x )² + 12² = 15²
[tex]\frac{1}{4}[/tex] x² + 144 = 225 ( subtract 144 from both sides )
[tex]\frac{1}{4}[/tex] x² = 81 ( multiply both sides by 4 to clear the fraction )
x² = 324 ( take the square root of both sides )
x = [tex]\sqrt{324}[/tex] = 18 → B
