Perimeter of square is 48 cm and length of a rectangle is equal to side of square and breadth of rectangle is 4 cm less than length of the rectangle. Find the area of rectangle.

The correct option is 96cm².

Let's solve the problem step-by-step.

Step 1: Find the side of the square

We are given that the perimeter of the square is 48 cm.

The formula for the perimeter of a square is:

$\text{Perimeter of square}=4\×\text{side}$

Substituting the given value:

$48=4\×\text{side}$

$\text{side}=\frac{48}{4}=12\text{cm}$

Step 2: Find the dimensions of the rectangle

1. Length of the rectangle is equal to the side of the square:

$\text{Length (l)}=12\text{cm}$

2. Breadth of the rectangle is 4 cm less than its length:

$\text{Breadth (b)}=12-4=8\text{cm}$

Step 3: Calculate the area of the rectangle

The formula for the area of a rectangle is:

$\text{Area of rectangle}=\text{Length}\×\text{Breadth}$

Substituting the length and breadth:

$\text{Area of rectangle}=12\×8=96{\text{cm}}^2$

Thus, the area of the rectangle is 96cm².