Question

Sides of a triangle are in the ratio of 12: 17: 25 and its area is 9000cm2. Find its perimeter.

Answer 1

Let the sides of the triangle be 12x, 17x and 25x

Perimeter of the triangle = 540 cm

∴ 12x + 17x + 25x = 540

⇒ 54x = 540 ⇒ x = 10

Let, a = 12x = 12 x 10 = 120 cm

b = 17x = 17 x 10 = 170 cm

c = 25x = 25 x 10 = 250 cm

s = (a + b + c)/2 = (120 + 170 + 250)/2 = 540/2

= 270 cm

∴Area of triangle = root under (√s(s -a) (s -b)(s -c))

=root under (√270(270 - 120)(270 - 170)(270 - 250))

= root under (√270 x 150 x 100 x 20)

= 100 under root(√27 x 15 x 20)

= 100 x 9 x 5 x 2

= 9000 cm2

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