Question

△abc and △xyz are similar. find the missing side length.
(the triangles are not drawn to scale.)

Explanation:

Step1: Identify Corresponding Sides

In similar triangles, corresponding sides are proportional. Let's match the sides: \( AC = 56 \) corresponds to \( XZ = 7 \), \( BC = 64 \) corresponds to \( YZ = 8 \), and \( AB \) (unknown) corresponds to \( XY = 5 \).

Step2: Set Up Proportion

Let the missing side \( AB = x \). The proportion is \( \frac{AB}{XY}=\frac{AC}{XZ} \) (or \( \frac{AB}{XY}=\frac{BC}{YZ} \), both work). Using \( \frac{x}{5}=\frac{56}{7} \).

Step3: Solve for \( x \)

Simplify \( \frac{56}{7}=8 \), so \( \frac{x}{5}=8 \). Multiply both sides by 5: \( x = 8\times5 = 40 \).

Answer:

40