Question

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

• A. 1000 sq.cm
• B. 5000 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,
12 x +17 x +25 x = 540 cm
54 x = 540 cm
x = 10
Therefore,
a = 12x = 12 $\times$ 10 = 120
b = 17x = 17 $\times$ 10 = 170
c = 25x = 25 $\times$ 10 = 250
Semi-perimeter, s, a, b and c in Heron's formula, we will get
$A=\sqrt{s(s-a)(s-b)(s-c)}A=\sqrt{270(270-120)(270-170)(270-250)}A=\sqrt{270\times 150\times 100\times 20}=9000sq.cm$