Question

The Perimeter of a Triangular Field is 420m and its sides are in the ratio 6:7:8. Find its Area.​

Answer 1

A ≈ 8133.27 m²

Explanation:

Sum the parts of the ratio 6 + 7 + 8 = 21 parts

Divide the perimeter by 21 to find the value of one part

420 ÷ 21 = 20 ← value of 1 part of the ratio, hence sides of triangle are

6 × 20 = 120

7 × 20 = 140

8 × 20 = 160

To calculate the area (A) we can use Hero's formula

A =
`√(s(s-a)(s-b)(s-c))`

Where s is the semi perimeter and a, b, c the sides of the triangle

let a = 120, b = 140 , c = 160 and s = 420 ÷ 2 = 210

A =
`√(210(210-120)(210-140)(210-160))`

=
`√(210(90)(70(50))`

=
`√(66150000)` ≈ 8133.27 m²