Perimeter of triangle = 540 cm
The ratio of sides of triangle = 12: 17: 25
Let, one of the sides of triangle a = 12 x
Therefore, remaining two sides are b = 17 x and c = 25x.
We know that the perimeter of triangle = a + b + c
⇒ 540 = 12 x + 17 x + 25 x
⇒ 540 = 54x
⇒ x = 540/54 = 10
So, the sides of triangle are a = 12 × 10 = 120 cm, b = 17 × 10 = 170 cm and c = 25 × 10 = 250 cm.
So, the semi- perimeter of triangle is given by
S = (a + b + c /2) = 540/2 = 270 cm
Therefore, using Heron’s formula, the area of triangle = √s(s – a)(s – b)(s – c)
= √270(270 – 120)(270 – 170)(270 – 250)
= √270(150)(100)(20)
= √81000000
= 9000 cm²
Hence, the area of triangle is 9000 cm².