Question

two triangles are similar. the ratio of their corresponding sides is $\frac{3}{5}$. if the shorter triangles perimeter is 24, find the perimeter of the larger triangle.

Explanation:

Step1: Set up the proportion

Let \( x \) be the perimeter of the larger triangle. For similar triangles, the ratio of perimeters is equal to the ratio of corresponding sides. So we have the proportion \(\frac{24}{x}=\frac{3}{5}\).

Step2: Cross - multiply

Cross - multiplying gives \(3x = 24\times5\).

Step3: Solve for \(x\)

First, calculate \(24\times5 = 120\). Then, \(x=\frac{120}{3}\).

Answer:

\(40\)