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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 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`
= 270 cm
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`
= `sqrt(10^2 xx 10^2 xx 3^2 xx 3^2 xx 5^2 xx 2^2) cm^2`
= (10 × 10 × 3 × 3 × 5 × 2) cm2
= 9,000 cm2
Therefore, the area of this triangle is 9,000 cm2.
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