Question

sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm.find its area.

Answer 1

Let the first side = 12a
Second side = 17a
Third side = 25a

Perimeter = 540
=> 12a + 17a +25a = 540
=> 54 a = 540
=> a = 10

First side = 120 cm

Second side = 170 cm

Third side = 250 cm

Semi Perimeter = 540/2 = 270 cm

(s-a) = 270 - 120 = 150

(s-b) = 270 - 170 = 100

(s-c) = 270 - 250 = 20


$area = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{270 \times 150 \times 100 \times 20 } \\ = 100 \sqrt{27 \times 15 \times 10 \times 2} \\ = 100 \sqrt{9 \times 9 \times 5 \times 5 \times 2 \times 2} \\ = 100 \times 3 \times 3 \times 5 \times 2 \\ = 9000 \: {cm}^{2}$