The area of a square is 900 cm². The length of a rectangle is twice the side of the square. If the perimeter of the rectangle is 216 cm, then find the breadth of the rectangle (in cm).

The correct answer is 48.

Let's break down the solution step-by-step:

Step 1: Calculate the side length of the square

The formula for the area of a square is:

$\text{Area}=s^2$

where $s$ represents the side of the square.

Given that the area of the square is 900 cm², we have:

$s^2=900$

Taking the square root on both sides:

$s=\sqrt{900}=30\text{cm}$

Step 2: Find the length of the rectangle

We are given that the length of the rectangle ($l$) is twice the side of the square ($s$):

$l=2\times s$

Substituting $s=30\text{cm}$ into the equation:

$l=2\times 30=60\text{cm}$

Step 3: Calculate the breadth of the rectangle

The perimeter of a rectangle is calculated using the formula:

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

where $b$ is the breadth of the rectangle.

Given that the perimeter is 216 cm and the length ($l$) is 60 cm, we substitute these values into the formula:

$216=2(60+b)$

Dividing both sides by 2:

$108=60+b$

Subtracting 60 from both sides to solve for $b$:

$b=108-60$

$b=48\text{cm}$

Therefore, the breadth of the rectangle is 48 cm.