Question

1. the shapes at right are similar.

a. what is the scale factor?
b. find the sides labeled ( x ) and ( y ).

Explanation:

Step1: Identify corresponding sides

Use the pair of known corresponding sides (24 and 8) to find the scale factor from the larger shape to the smaller shape.
$\text{Scale factor} = \frac{\text{Smaller side}}{\text{Larger side}} = \frac{8}{24} = \frac{1}{3}$

Step2: Solve for $x$

Set up proportion using scale factor.
$\frac{x}{8} = \frac{1}{3} \implies x = 8 \times \frac{1}{3} = \frac{8}{3}$

Step3: Solve for $y$

Set up proportion using scale factor.
$\frac{y}{5} = \frac{1}{3} \implies y = 5 \times \frac{1}{3} = \frac{5}{3}$

Answer:

a. $\frac{1}{3}$
b. $x = \frac{8}{3}$, $y = \frac{5}{3}$