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. For $\triangle ABC$ and $\triangle XYZ$, let's match the sides. Let $AB = 4$, $BC = 8$, $AC = 7$; $XY = 12$, $YZ = 24$, $XZ =?$

Find the scale factor: $\frac{XY}{AB}=\frac{12}{4}=3$.

Step2: Apply scale factor to AC

Since the triangles are similar, the ratio of corresponding sides is equal. So $XZ = AC\times$ scale factor.

$AC = 7$, scale factor $= 3$, so $XZ = 7\times3 = 21$.

Answer:

21