Perimeter of a rectangular field is equal to the perimeter of a triangular field whose sides are in the ratio 3:2:4 respectively. lf area of rectangular field is 500 m2 and sides are in the ratio 5:4 respectively, then calculate the longer side of the triangular field.

Calculation:

Let the sides of the rectangular field be 5x and 4x. The area of the rectangle is:

Area = 5x × 4x = 500

⇒ 20x² = 500

⇒ x² = 25

⇒ x = 5.

Thus, the length = 5x = 25 m, and the breadth = 4x = 20 m.

The perimeter of the rectangular field = 2 × (25 + 20) = 90 m.

The sides of the triangular field are in the ratio 3 : 2 : 4. Let the sides be 3y, 2y, and 4y.

The perimeter of the triangle is: 3y + 2y + 4y = 9y.

Since the perimeter is 90 m, we have: 9y = 90 ⇒ y = 10.

The longest side of the triangle is: 4y = 4 × 10 = 40 m.

∴ The longer side of the triangular field is 40 meters.