The ratio of length and breadth of a rectangle is 3 : 2 respectively. The ratio of its perimeter and area is 5 : 9. The breadth of the rectangle (in meters) is:

Correct option is D

Given :

Ratio of their length and breadth = 3 :2

Ratio of its perimeter and area = 5 : 9

Solution :

The length of rectangle will be = 3x

and the breadth of rectangle will be = 2x

Now the perimeter of rectangle = 2 ( 3x + 2x ) = 10x ...... Eq (1)

Area of rectangle = 3x × 2x = 6x² ....... Eq (2)

Now the ratio of its perimeter and area is given as 5 : 9

So we can form the equation by using Eq (1) and Eq (2 ) as :

​$$=> \frac{10x }{ 6x^2}= \frac{5 }{ 9} \\\ \\=> \frac{5 }{3x }= \frac{5 }{ 9}$$​​

=> x = 3

Hence the breadth of rectangle will be :

=> 2 × 3 = 6 metre

Hence the correct answer is "6 metre".