Question

find the unknown side length labeled with a variable in the given pair of similar triangles.
10
15
21
x
x =
(simplify your answer.)

Explanation:

Step1: Identify similar triangles property

Since the triangles are similar, their corresponding sides are proportional. The legs and hypotenuses of the right triangles correspond. So, we set up the proportion: $\frac{10}{x}=\frac{15}{21}$.

Step2: Solve for x

Cross - multiply: $15x = 10\times21$. Calculate $10\times21 = 210$. Then, $x=\frac{210}{15}$. Simplify $\frac{210}{15}=14$.

Answer:

14