Question

find the unknown side lengths labeled with a variable in the given pair of similar triangles.
a = cm
b = cm

Explanation:

Step1: Set up proportion for side - a

Since the triangles are similar, the ratios of corresponding sides are equal. For side \(a\), we have the proportion \(\frac{a}{15}=\frac{5}{15}\).

Step2: Solve for \(a\)

Cross - multiply: \(15a = 5\times15\), then \(a=\frac{5\times15}{15}=5\).

Step3: Set up proportion for side - b

For side \(b\), the proportion is \(\frac{b}{18}=\frac{5}{15}\).

Step4: Solve for \(b\)

Cross - multiply: \(15b = 5\times18\), then \(b=\frac{5\times18}{15}=6\).

Answer:

\(a = 5\) cm
\(b = 6\) cm