The area of a triangular field whose sides are 96 m, 110 m, and 146 m is equal to the area of a rectangular park whose sides are in the ratio 3 : 2. What is the perimeter(in m ) of the rectangular park?

$40\sqrt{55}$

We know that,

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

Area of rectangle = length × breadth

Sides of triangular field = 96m, 110m and 146m

Area of triangular field = \(\frac{1}{2}\) × 96 × 110 = 5280 m²

Area of rectangular field = 5280 m²

Let length and breadth of rectangular field be 3a and 2a respectively.

= 3a × 2a = 5280

= a = 4\(\sqrt {55}\) m

Length and breadth of rectangular field = 12\(\sqrt {55}\) m and 8\(\sqrt {55}\) m respectively.

Perimeter of rectangular field = 2 × (12\(\sqrt {55}\) + 8\(\sqrt {55}\)) = 40\(\sqrt {55}\)m