Question

Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm.Find its area.

Answer 1

Let the common ratio between the sides of the given triangle be x. Therefore, the sides of the triangle will be $12x,17x$ and $25x.$
Perimeter of this triangle = 540cm
$12x+17x+25x=540cm$ i,e $54x=540cm$

$\therefore x=10cm$

Sides of the triangle will be 120 cm, 170 cm, and 250 cm. $s=\frac{Perimeteroftriangle}{2}=\frac{540cm}{2}=270cm$

By Heron’s formula,

Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{270(270-120)(70-170)(270-250)c{m}^2}=\sqrt{270\times 150\times 100\times 20}c{m}^2=9000c{m}^2$

Therefore, the area of this triangle is $9000c{m}^2$