Question

Sides of a triangle are in the ratio of 12:17:25 and it's perimeter is 540cm. Find the area.(using herons Formula)

Answer 1

Let sides of tr. be 12n,17n,25n
Perimeter=540
12n+17n+25n=540
n=10
Sides are 120,170,250
s=540/2=270
Area=√270*(270-120)*(270-170)*(270-250)
Solving this u can get answer
900cm^2

Answer 2

Given :-

Sides of a triangles are in the ratio of 12:17:25 and it's perimeter is 540cm.

To Find :-

Area

Solution :-

Let the sides be 12x, 17x and 25x

Perimeter = a + b + c

540 = 12x + 17x + 25x

540 = 54x

540/54 = x

10 = x

Therefore

Sides are

12x = 12(10) = 120 cm

17x = 17(10) = 170 cm

25x = 25(10) = 250 cm

Now

Semiperimeter = Perimeter/2

Semiperimeter = 540/2

Semiperimeter = 270 cm

Now

Area = √s(s - a)(s - b)(s - c)

Area = √270(270 - 120)(270 - 170)(270 - 250)

Area = √270 × 150 × 100 × 20

Area = √(8,10,00,000)

Area = 9000 cm²

Therefore

Area of triangle is 9000 cm²