Sides of a triangle are in the ratio of 12:17:25 and its perimeter is $ 540 \mathrm{~cm} $. Find its area.

AcademicMathematicsNCERTClass 9


The sides of a triangle are in the ratio of $12: 17: 25$ and its perimeter is $540\ cm$.

To find:

We have to find the area of the triangle.


Let the common ratio between the sides of the triangle be  $=\ a$

This implies,

The sides of the triangle as $12\ a, 17\ a$ and $25\ a$.

We know that,

Perimeter $P$ of a triangle with sides of length $a$ units, $b$ units and $c$ units 


We have perimeter as $540\ cm$.

This implies,

$540\ cm=12\ a+17\ a+25\ a$

$540\ cm=54\ a$

This implies,

$a\ cm=\frac{540}{54}$

$a\ cm=10\ cm$


The sides of the triangle are $12\times10\ cm=120\ cm, 17\times\ 10\ cm=170\ cm$ and $25\times10\ cm=250\ cm$

By Heron's formula:






$S=270\ cm$

This implies,



$A=9000\ cm^2$


The area of the triangle is $9000\ cm^2$.

Updated on 10-Oct-2022 13:41:58