Question

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

• A. 5000 sq. cm
• B. 6000 sq. cm
• C. 9000 sq. cm
• D. 8000 sq. cm

Answer 1

The correct option is C 9000 sq. cm

Explanation: The ratio of the sides is 12: 17: 25

Perimeter = 540 cm

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

Hence,

12x + 17x + 25x = 540 cm

54x = 540 cm

x = 10

Therefore,

a = 12x = 12 x 10 = 120
b = 17x = 17 x 10 = 170
c = 25x = 25 x 10 = 250

Semi-perimeter, s$=\frac{540}{2}=$ 270 cm

Putting the values of s, a, b and c in Heron’s formula, we will get

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{270(270-120)(270-170)(270-250)}$

$A=\sqrt{270\times 150\times 100\times 20}=9000$ sq. cm