Question

these 2 triangles are similar. find side lengths a and b. note: the 2 figures are not drawn to scale.

Explanation:

Step1: Set up proportion for side \(a\)

Since the triangles are similar, \(\frac{9}{3}=\frac{a}{5}\)

Step2: Solve for \(a\)

Cross - multiply: \(3a = 9\times5\), so \(a=\frac{9\times5}{3}=15\)

Step3: Set up proportion for side \(b\)

\(\frac{9}{3}=\frac{b}{21}\)

Step4: Solve for \(b\)

Cross - multiply: \(3b=9\times21\), so \(b = \frac{9\times21}{3}=63\)

Answer:

\(a = 15\), \(b = 63\)