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 side of the triangle will be 12x, 17x, and 25x. 
Perimeter of this triangle = 540 cm 
12x + 17x + 25x = 540 cm 
\(⇒\) 54x = 540
x = \(\frac{540}{54}\)
x = 10 cm
The sides of the triangle:
12x = 12 × 10 = 120 cm,
17x = 17 × 10 = 170 cm, 
25x = 25 × 10 = 250 cm
a = 120cm, b = 170 cm, c = 250 cm
Semi-perimeter(s) = \(\frac{540}{2}\) = 270 cm
By Heron’s formula,
Area of a triangle =\( \sqrt{\text{s(s - a)(s - b)(s - c)}}\)
\(= \sqrt{\text{270(270 - 120)(270 - 170)(270 - 250)}}\)
\(= \sqrt{\text{270 × 150 × 100 × 20}}\)
\(= \sqrt{81000000}\)
= 9000 cm²
Area of the triangle = 9000 cm².