The ratio of area of a square and area of a rectangle is 3:2 respectively. The side of square is equal to length of the rectangle. The perimeter of the rectangle is 40 meters, then find the breadth of the rectangle?

The correct option is 8 m.

Step-by-step Explanation:

Let the side of the square be s, the length of the rectangle be l, and the breadth of the rectangle be b.

According to the question, the side of the square is equal to the length of the rectangle:

$s=l$

Step 1: Use the ratio of areas to find the relationship between length and breadth.

The area of the square is given by:

$\text{Area of square}=s^2=l^2$

The area of the rectangle is given by:

$\text{Area of rectangle}=l\times b$

We are given that the ratio of the area of the square to the area of the rectangle is 3 : 2:

$\frac{l^2}{l\times b}=\frac{3}{2}$

Simplifying the left side by dividing the numerator and denominator by l:

$\frac{l}{b}=\frac{3}{2}$

Therefore, we get:

$l=\frac{3}{2}b$

Step 2: Use the perimeter of the rectangle to find the breadth.

The formula for the perimeter of a rectangle is:

$\text{Perimeter}=2(l+b)$

We are given that the perimeter of the rectangle is 40 meters:

$2(l+b)=40$

$l+b=20$

Now, substitute $l=\frac{3}{2}b$ into the equation:

$\frac{3}{2}b+b=20$

$\frac{5b}{2}=20$

$5b=40$

$b=8$

Thus, the breadth of the rectangle is 8 meters.