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Question

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 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×x=12×10=120 cm17×x=17×10=170 cm25×x=25×10=250 cm

s=Perimeter of triangle2=540 cm2=270 cm

By Heron’s formula,

Area of the given triangle=s(sa)(sb)(sc)

=270(270120)(270170)(270250) cm2
=270×150×100×20 cm2

=9,000 cm2

Therefore, the area of this triangle is 9,000 cm2

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