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Question

Find the area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter of the triangle is 270 m.


A

2150 m2

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B

2250 m2

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C

2350 m2

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D

2450 m2

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Solution

The correct option is B

2250 m2


The area (A) of a triangle can be calculated using Heron's formula, given by:
A=s(sa)(sb)(sc),
where a, b and c are its sides and s is its semi-perimeter.
[i.e., s=a+b+c2]

Given, the sides are in the ratio 12:17:25 and the perimeter is 270 m.
Let the common factor be ‘x’
Then, 12x+17x+25x=270
54x=270
x=5
The lengths of the sides are 60 m, 85 m and 125 m.
Then,
s=(60+85+125)2 = 135 m
A=s(sa)(sb)(sc)=135(13560)(13585)(135125)=135×75×50×10=5×9×3×25×3×25×2×5×2=5×9×25×2=2250 m2


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