A rectangular flower bed is 7 m long. If the boundary around the bed is 22 m long, find its breadth. Also, find its area.

Answer

To solve the problem step by step, we will follow the given information and apply the formulas for perimeter and area of a rectangle.

### Step 1: Understand the given information
We know:
- Length (L) of the rectangular flower bed = 7 m
- Perimeter (P) of the flower bed = 22 m

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (L + B) \]
where L is the length and B is the breadth.

### Step 3: Substitute the known values into the perimeter formula
We can substitute the known values into the formula:
\[ 22 = 2 \times (7 + B) \]

### Step 4: Simplify the equation
Now, we simplify the equation:
1. Divide both sides by 2:
\[ 11 = 7 + B \]

### Step 5: Solve for the breadth (B)
Now, we can isolate B:
\[ B = 11 - 7 \]
\[ B = 4 \, \text{m} \]

### Step 6: Find the area of the rectangle
The formula for the area (A) of a rectangle is:
\[ A = L \times B \]
Substituting the values of L and B:
\[ A = 7 \times 4 \]
\[ A = 28 \, \text{m}^2 \]

### Final Answers
- The breadth of the flower bed is **4 m**.
- The area of the flower bed is **28 m²**.

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