Question

$△\text{ABC}\sim \Delta \text{XYZ and the ratio of the}$$\text{corresponding sides of}\Delta \text{XYZ}\text{and}\Delta \text{ABC}$ $\text{is 3 : 1. Find the measure of sides XY, YZ}$
$\text{and ZX.}$

• A. 36 in, 27 in, and 55 in
• B. 36 in, 27 in, and 45 in
• C. 36 in, 21 in, and 45 in
• D. 36 in, 33 in, and 45 in

Answer 1

The correct option is B 36 in, 27 in, and 45 in

Given:
$△\text{ABC}\sim \Delta \text{XYZ}$

$\frac{XY}{AB}=\frac{YZ}{BC}=\frac{XZ}{AC}=3$

$⟹\frac{XY}{12}=\frac{YZ}{9}=\frac{XZ}{15}=3$

$⟹\text{XY = 36 in, YZ = 27 in and}$
$\text{XZ = 45 in.}$