Question

sides of a triangle are in the ratio of 12 ratio 17 ratio 25 and its perimeter is 540 cm find its area by heron's formula

Answer 1

Ratio of side 1 : side 2 : side 3 = 12 : 17 : 25 (Given)

Define x:

Let x be the constant ratio

side 1 : side 2 : side 3 = 12x : 17x : 25x

Solve x:

Given that the perimeter is 540

12x + 17x + 25x = 540 cm

54x = 540

x = 10

Find the length of the sides:

Side 1 = 12x = 12(0) = 120 cm

Side 2 = 17x = 17(10) = 170 cm

Side 3 = 25x = 25(10) = 250 cm

Find the semiperimeter:

p = perimeter ÷ 2

p = 540 ÷ 2 = 270 cm

Find the area:

area = √p(p - a)(p - b)(p - c)

area = √270(270 - 120)(270 - 170)(270 - 250)

area = √81,000,000

area = 9000 cm²

Answer: The area of the triangle is 9000 cm²