Question

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

Answer 1

let the sides of the triangle be
12x +17x +25x =540
54x = 540
540/54 = x
10 = x
substitute x in 12x , 17x and 25x u get 120cm,170cm,250cm
now using heron's formula u can find the area
the area is 9000 square cm

Answer 2

Let,
In ∆ABC,
AB:BC:AC=12:17:25 & Perimeter of ∆ABC=540 cm
Suppose,
AB=12x,BC=17x & AC=25x.

Perimeter of ∆ABC=AB+BC+AC
540=12x+17x+25x
540=54x
x=10

AB=12x=12(10)=120 cm
BC=17x=17(10)=170 cm
AC=25x=25(10)=250 cm

Using Herons formula,

s=perimeter/2=540/2=270 cm

ABC=√(s(s-AB)(s-BC)(s-AC))
=√(270(270-120)(270-170)(270-250))
=√(270(150)(100)(20)
=√(8100000)
=900√10 cm^2