Question

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

Answer 1

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

According to the question, Let the sides in meters are a = 6x, b = 7x and c = 8x.

So, perimeter of the  triangle = 6x + 7x + 8x

420 = 21x

x = `420/21`

x = 20

Since, the sides of the triangular field are a = 6 × 20 cm = 120 m, b = 7 × 20 m = 140 m and c = 8 × 20 m = 160 m.

Now, semi-perimeter(s) of triangle will be:

`s = 1/2 xx 420  m` 

= 210 m

Area of the triangle field = `sqrt(s(s - a)(s - b)(s - c))`  ...[Using Heron’s formula]

= `sqrt(210(210 - 120)(210 - 140)(210 - 160))`

= `sqrt(210 xx 90 xx 70 xx 50)`

= `100sqrt(7 xx 3 xx 3^2 xx 7 xx 5)`

= `100 xx 7 xx 3 xx sqrt(15)`

= `2100sqrt(15)`

Therefore, the area of the triangular field is `2100sqrt(15)`.