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

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#### Solution

Let the common ratio between the sides of the given triangle be *x*.

Therefore, the side of the triangle will be 12*x*, 17*x*, and 25*x*.

Perimeter of this triangle = 540 cm

12*x* + 17*x* + 25*x* = 540 cm

54*x* = 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))`

`=[sqrt(270(270-120)(270-170)(270-250))]cm^2`

`=[sqrt(270xx150xx100xx20)]cm^2`

= 9000 cm^{2}

Therefore, the area of this triangle is 9000 cm^{2}.

Concept: Area of a Triangle by Heron's Formula

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