Question

△abc and △xyz are similar. find the missing side length.
image of two triangles: △abc with sides ab=32, bc=56, ac=40; △xyz with sides xy=4, xz=5, yz=?

Explanation:

Step1: Find the scale factor

The corresponding sides \( AB = 32 \) and \( XY = 4 \). The scale factor from \( \triangle ABC \) to \( \triangle XYZ \) is \( \frac{XY}{AB}=\frac{4}{32}=\frac{1}{8} \).

Step2: Apply the scale factor to find the missing side

The side \( BC = 56 \) in \( \triangle ABC \). Let the missing side (corresponding to \( BC \)) in \( \triangle XYZ \) be \( x \). Then \( x = BC\times\frac{1}{8}=56\times\frac{1}{8} = 7 \).

Answer:

7