Question

The perimeter of a triangular ground is 420m and its sides are in the ratio 6:7:8.find the area of the triangular ground

Answer 1

Solution -

Perimeter of the triangular ground = 420m

Sides are given as 6 : 7 : 8 = 6x : 7x : 8x .......where x is the multiplyer

Given:

6x + 7x + 8x = 420

21x = 420

x = 20

Therefore, sides of the triangular ground are 6x = 6 * 20 = 120m, 7x = 7 * 20 = 140m, and 8x = 8 * 20 = 160m

Area of the triangle whose three sides are given is given by Heron's formula.

A = sqrt (s * (s - a) (s - b) (s - c)) ------------where s = 420/2 = 210 is the half perimeter 
  
    = sqrt (210 * (210 - 120) * (210 - 140) * (210 - 160))
  
    = sqrt ( 210 * 90 * 70 * 50)
   
    = sqrt (66150000)
 
    = sqrt (6615 * 10000)
    = 100 * sqrt (49 * 135)

    = 100 * 7 * sqrt (135)
    = 700 * sqrt (135)
  
 Area of the triangular ground = 700 * sqrt (135) sq.m

Answer 2

Hope it helps...... ...Ans in above pic