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

Q5.    Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

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Given the sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm

Let us consider the length of one side of the triangle be a = 12x

Then, the remaining two sides are b = 17x and c = 25x.

So, by the given perimeter, we can find the value of x:

Perimeter = a+b+c = 12x+17x+25x = 540cm

\implies 54x = 540cm

\implies x = 10

So, the sides of the triangle are:

a = 12\times10 =120 cm

b = 17\times10 =170 cm

c = 25\times10 =250 cm

So, the semi perimeter of the triangle is given by

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

Therefore, using Heron's Formula, the area of the triangle is given by

A = \sqrt{s(s-a)(s-b)(s-c)}

     = \sqrt{270(270-120)(270-170)(270-250)}

     = \sqrt{270(150)(100)(20)}

     = \sqrt{81000000} = 9000cm^2

Hence, the area of the triangle is 9000cm^2.

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