Question

find the value of x using the figure to the right.
x = \square (simplify your answer.)

Explanation:

Step1: Identify similar triangles

The two right triangles are similar by AA similarity (share an acute angle, both have right angles). Corresponding sides are proportional: $\frac{x}{15} = \frac{15}{16}$

Step2: Solve for x

Cross-multiply to isolate x:
$x = \frac{15 \times 15}{16}$

Step3: Simplify the expression

Calculate the numerator:
$x = \frac{225}{16}$

Answer:

$\frac{225}{16}$