Question

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

Answer 1

This might help you   Please go through it

Answer 2

$\bf \LARGE \it Hey \: User!!!$

given the sides of the triangle in the ratio of 12 : 17 : 25

let the sides be 12x, 17x and 25x.

given the perimeter of the triangle = 540cm
therefore 12x + 17x + 25x = 540cm
>> 54x = 540cm
>> x = 540/54
>> x = 10

therefore the sides of the triangle are :-

◾12x = 12 × 10 = 120cm
◾17x = 17 × 10 = 170cm
◾25x = 25 × 10 = 250cm

semi-perimeter of the triangle = 540/2 = 270cm

let the sides of the triangle be a, b and c.

heron's formula = √s(s - a)(s - b)(s - c)

◾(s - a) = 270 - 120 = 150cm
◾(s - b) = 270 - 170 = 100cm
◾(s - c) = 270 - 250 = 20cm

therefore area of the triangle = √(270 × 150 × 100 × 20)
= √81000000
= 9000cm²

$\bf \LARGE \it Cheers!!!$