Question

The side of triangle in the ratio 12:17:25 and its perimeter is 540m.
Find its area using herons formula
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Answer 1

Let,

a be 12x

b be 17x

c be 25x

Therefore,

Perimeter = 540 cm

=> a + b + c = 540

=> 12x + 17x + 25x = 540

=> 54x = 540

=> x = 540/54

=> x = 10

.°. x = 10 cm

.°. a = 12x = 120 cm

b = 17x = 170 cm

c = 25x = 250 cm

.°. s = 540/2 = 270 cm

.°. Area

= √{s(s - a)(s - b)(s - c)}

= √{270(270 - 120)(270 - 170)(270 - 250)}

= √(270 × 150 × 100 × 20)

= √(3 × 3 × 3 × 2 × 5 × 3 × 5 × 2 × 5 × 2 × 5 × 2 × 5 × 2 × 2 × 5)

= √(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5 × 5 × 5 × 5)

= 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5

= 9800 cm²