Question

the lengths of the sides of a triangle are in the ratio of 4 : 5 : 3 and its perimeter is 96 cm. Find its area

Answer 1

let the ratio as
4x
5x
3x
perimeter of triangle =4x+5x+3x
96=12x
96÷12=x
8=x
then , according to question
4x= 32cm
5x=40cm
3x=24cm
area of triangle =

Answer 2

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let the sides of the triangle be 4x, 5x and 3x respectively.
perimeter of triangle = sum of all the sides
96 = 4x+ 5x+ 3x
96 = 12x
96/12 = x
8 = x
hence, 4x = 4 × 8 = 32 cm
              5x = 5 × 8 = 40 cm
              3x = 3 × 8 = 24cm
semi-perimeter of triangle = perimeter/2
                                              = 96/2
                                               = 48 cm.
acc. to heron's formula,area of triangle = [48(48-32)(48-40)(48-24)]^{1/2} 
                                                                    = [404 cm]^{2} 

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