Question

△abc and △xyz are similar. find the missing side length.
(the triangles are not drawn to scale.)
triangle abc: ab = 4, ac = 5, bc = ?
triangle xyz: xy = 36, xz = 45, yz = 63

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{AC}{XZ} = \frac{5}{45} = \frac{1}{9}$

Step2: Relate sides via ratio

Let missing side $BC = x$. $\frac{x}{YZ} = \frac{1}{9}$

Step3: Solve for missing side

$x = \frac{YZ}{9} = \frac{63}{9}$

Answer:

7