The perimeter of a triangular field is 144 m and the ratio of the sides is 3:4:5. Find the area of the field.

Explanation

Let the side of the triangle, `a,b and c be 3x,4x,5x`
Perimeter=144m
`3x+4x+5x=144`
`=>12x=144,x=12`
`a=12×3=36m`
`b=4×12=48m`
`c=5×12=60`
Then,` s=1/2(a+b+c)`
`=1/2(36+48+60)`
`=1/2(144)=72`
Area of the triangle`=sqrt(s(s−a)(s−b)(s−c))`
`=>sqrt(72(72−36)(72−48)(72−60))`
`sqrt(72xx36xx24xx12)=864 m^2`