If the perimeter of a rectangle is `24` units and the length exceeds the breadth by `4` units, then find the area of a rectangle .

Answer

To solve the problem step by step, we will use the information provided about the perimeter and the relationship between the length and breadth of the rectangle.

### Step 1: Understand the given information
We know that:
- The perimeter of the rectangle is 24 units.
- The length (L) exceeds the breadth (B) by 4 units.

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]

### Step 3: Set up the equation using the perimeter
Since the perimeter is 24 units, we can write:
\[ 2(L + B) = 24 \]

### Step 4: Simplify the perimeter equation
Dividing both sides of the equation by 2 gives us:
\[ L + B = 12 \]
This is our first equation.

### Step 5: Express length in terms of breadth
We are also given that the length exceeds the breadth by 4 units:
\[ L = B + 4 \]
This is our second equation.

### Step 6: Substitute the expression for L into the first equation
Now, we can substitute the expression for L from the second equation into the first equation:
\[ (B + 4) + B = 12 \]

### Step 7: Combine like terms
Combining the terms gives us:
\[ 2B + 4 = 12 \]

### Step 8: Solve for B
Subtract 4 from both sides:
\[ 2B = 12 - 4 \]
\[ 2B = 8 \]
Now, divide by 2:
\[ B = 4 \]

### Step 9: Find the length using the value of breadth
Now that we have the breadth, we can find the length using the second equation:
\[ L = B + 4 = 4 + 4 = 8 \]

### Step 10: Calculate the area of the rectangle
The area (A) of a rectangle is given by:
\[ A = L \times B \]
Substituting the values of L and B:
\[ A = 8 \times 4 = 32 \]

### Final Answer
The area of the rectangle is \( 32 \) square units.

---