$ \triangle \mathrm{ABC} \sim \triangle \mathrm{ZYX} . $ If $ \mathrm{AB}=3 \mathrm{~cm}, \quad \mathrm{BC}=5 \mathrm{~cm} $, $ \mathrm{CA}=6 \mathrm{~cm} $ and $ \mathrm{XY}=6 \mathrm{~cm} $, find the perimeter of $ \Delta \mathrm{XYZ} $.


Given:

\( \triangle \mathrm{ABC} \sim \triangle \mathrm{ZYX} . \)

\( \mathrm{AB}=3 \mathrm{~cm}, \mathrm{BC}=5 \mathrm{~cm} \), \( \mathrm{CA}=6 \mathrm{~cm} \) and \( \mathrm{XY}=6 \mathrm{~cm} \)

To do:

We have to find the perimeter of \( \Delta \mathrm{XYZ} \).

Solution:

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

When two triangles are similar their corresponding angles are equal and corresponding angles are equal and corresponding sides are in proportion.

Therefore,

$\frac{AB}{ZY}=\frac{BC}{YX}=\frac{AC}{ZX}$

This implies,

$\frac{AB}{ZY}=\frac{BC}{YX}$

$\frac{3}{ZY}=\frac{5}{6}$

$ZY=\frac{3\times6}{5}$

$YZ=\frac{18}{5}\ cm$

$\frac{BC}{YX}=\frac{AC}{ZX}$

$\frac{5}{6}=\frac{6}{ZX}$

$ZX=\frac{6\times6}{5}$

$ZX=\frac{36}{5}\ cm$

The perimeter of \( \Delta \mathrm{XYZ}=6+\frac{18}{5}+\frac{36}{5} \)

$=\frac{6\times5+18+36}{5}\ cm$

$=\frac{84}{5}\ cm$

Hence, the perimeter of \( \Delta \mathrm{XYZ} \) is $\frac{84}{5}\ cm$.

Tutorialspoint
Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

37 Views

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements