Question

(This question is from Heron's Formula) Any Genius here???

The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300m. Find its area.

Answer 1

Given Perimeter = 300
We know that sum of sides = Perimeter
Side ratio = 3:5:7
Hence, 3+5+7====300
15===300
1===20
Sides = 3*20, 5*20, 7*20
          = 60, 100, 140
Semi perimeter ,s = 300/2 = 150
Heron's formula:
Area = root[s*(s-a)*(s-b)*(s-c)]
         = root[150*(150-60)*(150-100)*(150-140)
         = root[150*90*50*10]
         = root[15*10*9*10*5*10*10]
        = root[15*3^2*10^2*5*10^2]
        = 3*10*10* root[15*5]
       = 300* root[5*3*5]
       = 1500 root 3
hence Area = 1500*root3 m^2
Hope it helps