$ \Delta \mathrm{ABC} \sim \Delta \mathrm{XZY} $. If the perimeter of $ \triangle \mathrm{ABC} $ is $ 45 \mathrm{~cm} $, the perimeter of $ \triangle \mathrm{XYZ} $ is $ 30 \mathrm{~cm} $ and $ \mathrm{AB}=21 \mathrm{~cm} $, find $ \mathrm{XY} $.

Given:

\( \Delta \mathrm{ABC} \sim \Delta \mathrm{XZY} \).

The perimeter of \( \triangle \mathrm{ABC} \) is \( 45 \mathrm{~cm} \), the perimeter of \( \triangle \mathrm{XYZ} \) is \( 30 \mathrm{~cm} \) and \( \mathrm{AB}=21 \mathrm{~cm} \).

To do:

We have to find \( \mathrm{XZ} \).

Solution:

\( \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} \)

The ratio of the perimeters of two similar triangles is same as the ratio of their corresponding sides.

Therefore,

$\frac{Perimeter\ of\ \triangle ABC}{Primeter\ of\ \triangle XYZ}=\frac{AB}{XY}$

This implies,

$\frac{45}{30}=\frac{21}{XY}$

$XY=\frac{21\times30}{45}$

$XY=14\ cm$

Hence, \( \mathrm{XZ}=14\ cm \).