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:

Perimeter of triangular plot = 12 + 35 + 37 = 84 m

Half of the perimeter = s = 42 m

Area of the triangular plot = $$\sqrt{42\left(42-12\right)\left(42-35\right)\left(42-37\right)}$$

= $$\sqrt{42\left(30\right)\left(7\right)\left(5\right)}$$

= 210 cm$$^2$$

The area of a triangular plot is equal to the area of a rectangular field.

Area of a rectangular field = 210 cm$$^2$$

Sides of rectangular filed are in the ratio 7:3.

Let the sides of the rectangular field are 7p and 3p respectively.

7p x 3p = 210

p$$^2$$ = 10

p = $$\sqrt{10}$$

Perimeter of the rectangular field = 2(7p + 3p)

= 20p

= 20$$\sqrt{10}$$ cm

Hence, the correct answer is Option A