The area of a triangular field whose sides are 65 m, 72 m, and 97 m is equal to the area of a rectangular park whose sides are in the ratio of 5 : 13. What is the perimeter (in m ) of the rectangular park?

216

We know that,

Area of triangle = \(\frac{1}{2}\) × base × height 

Area of rectangle = length × breadth

Perimeter of rectangle = 2(l + b)

Given,

Length of triangle = 97 m

Base of a triangle =65 m

Height of triangle = 72 m

Ratio of length and breadth of a rectangle = 5 : 13

According to the question

= (\(\frac{1}{2}\) × 65 × 72) = (5x × 13x)

= (65 × 36) = 65x²

= x² = (\(\frac{(65 × 36) }{65}\)

= x² = 36

= x = 6 m

So the perimeter of rectangle = 2(5x + 13x)

= (2 × 18x) = 36x

= (36 × 6) = 216 m