Question

find the unknown side lengths labeled with a variable in the given pair of similar triangles.
a =
(simplify your answer. type a whole number.)

Explanation:

Step1: Identify the ratio of corresponding sides

Since the triangles are similar, the ratios of corresponding sides are equal. The ratio of the legs \( AB \) and \( PQ \) is \( \frac{12}{18}=\frac{2}{3} \).

Step2: Set up the proportion for the hypotenuses

Let the hypotenuse of the first triangle be \( BC = 20 \) and the hypotenuse of the second triangle be \( QR=a \). The proportion is \( \frac{20}{a}=\frac{2}{3} \).

Step3: Solve for \( a \)

Cross - multiply: \( 2a = 20\times3 \)
\( 2a=60 \)
Divide both sides by 2: \( a=\frac{60}{2}=30 \)

Answer:

\( 30 \)