The area of a triangular plot having sides 12 m, 35 m and 37 m is equal to the area of a rectangular field whose sides are in the ratio 7 : 3. The perimeter (in m) of the field is:

$20 \sqrt{10}$

We know that,

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

Perimeter of rectangle = 2(l + b)

Area of rectangle = (l × b)

We have,

Sides of a triangle = 12 m, 35 m and 37 m

This is a right angled triangle so,

The ratio of area of a rectangular field = 7 : 3

Area of right angled triangle = \(\frac{1}{2}\) × 12 × 35  = 6 × 35 = 210 m²

Area of rectangle = (7a × 3a) = 210

= 21a² = 210

= a² = 10

= a = \(\sqrt {10}\) m

Now,

Perimeter of rectangle = 2(7x + 3x)

⇒ 2 × 10x = 2 × 10\(\sqrt {10}\) = 20\(\sqrt {10}\)