Question

The ratio of sides of a triangle is 12 : 17 : 25 and its perimeter is 540 cm. Find the area of the triangle. (by heron's formula)

Answer 1

let the sides of triangle be 12x,17x&25x
perimeter =sum of all sides
p=12x+17x+25x
540=54x
x=10
sides of triangle =120,170&250
area of triangle
s=540/2
=270
area of triangle=√270×(270-120)×(270-170)×270-250)
=√270×150×100×20
√3×3×3×5×2×3×5×5×2×5×5×2×2×2×5×2
=3×3×5×5×5×2×2×2√5
=2000√5 is the area of triangle.

Answer 2

by using herons formula

S = perimeter/2

= 540/2 = 270

area = √s (s - a ) ( s - b ) ( s - c )

= put all value of above

a , b , C

√270 × 150 × 100 × 20

solve this

= 9000 cm^2