Question

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

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

Answer 1

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

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

Ratio of sides of △XYZ to sides of △ABC is 1:3

So,

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

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

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