Question

Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. 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 = 540 cm
12x + 17x + 25x = 540 cm
i.e., 54x = 540 cm
So, x = 10 cm

Sides of the triangle will be
$12\times x=12\times 10=120cm17\times x=17\times 10=170cm25\times x=25\times 10=250cm$

$s=\frac{Perimeteroftriangle}{2}=\frac{540cm}{2}=270cm$

By Heron’s formula,

$\text{Area of the given triangle}=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{270(270-120)(270-170)(270-250)}c{m}^2$
$=\sqrt{270\times 150\times 100\times 20}c{m}^2$

$=9,000c{m}^2$

Therefore, the area of this triangle is $9,000c{m}^2$