The perimeter of a triangular field is `450\ m` and its sides are in the ratio `13 : 12 : 5.` Find the area of the triangle.

Explanation

Let sides are `12 x, 13x and 5x`.
As `12,13 and 5` are pythagorean triplets, it is a right angled triangle.
Given that perimeter = `450m`
`12x + 13x + 5x=450`
`30x=450`
` x = (450/30) = 15`
As it is a right angled triangle, area of triangle is `(1/2)` xx base height = `(1/2)` xx product of small sides
` Area = (1/2) * 12x * 5x `
` Area = 6*5*x*x = 30 x² `
`Area = 30(15)² = 30(225) = 6750 m²`.