Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area.
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 cm
x = 10 cm
Sides of the triangle will be 120 cm, 170 cm, and 250 cm.
`s="perimeter of triangle"/2=540/2=270cm`
By Heron's formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
= 9000 cm2
Therefore, the area of this triangle is 9000 cm2.
Concept: Area of a Triangle by Heron's Formula
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