The length and breadth of a rectangle are in the ratio 3 : 2. If its perimeter is 730 cm, what is the area of the rectangle?

Given,

The length and breadth of the rectangle are in the ratio 3 : 2

Let the length and breadth of the rectangle are 3p and 2p respectively

Perimeter of the rectangle = 730 cm

$$=$$>  $$2\left(3p+2p\right)=730$$

$$=$$>  $$2\left(5p\right)=730$$

$$=$$>  $$10p=730$$

$$=$$>  $$p=73$$

$$\therefore\ $$Area of the rectangle = $$3p\times2p$$

$$=6p^2$$

$$=6\left(73\right)^2$$

$$=6\left(5329\right)$$

$$=31974  cm^2$$

Hence, the correct answer is Option A