The ratio of the length to the perimeter of a rectangle is 3:8. Find its dimensions, given that its perimeter is 32 m. Also, find its area.

Answer

To solve the problem step by step, we will follow the given information and apply the necessary formulas.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
We know that the ratio of the length (L) to the perimeter (P) of a rectangle is given as 3:8. This can be expressed mathematically as:
\[ \frac{L}{P} = \frac{3}{8} \]

2. **Using the Given Perimeter**:
We are also given that the perimeter (P) of the rectangle is 32 meters. Therefore, we can substitute this value into the equation:
\[ \frac{L}{32} = \frac{3}{8} \]

3. **Finding the Length**:
To find the length (L), we can cross-multiply:
\[ 8L = 3 \times 32 \]
Simplifying the right side:
\[ 8L = 96 \]
Now, divide both sides by 8:
\[ L = \frac{96}{8} = 12 \text{ meters} \]

4. **Finding the Breadth**:
The formula for the perimeter of a rectangle is:
\[ P = 2(L + B) \]
We know the perimeter is 32 meters, so we can set up the equation:
\[ 32 = 2(12 + B) \]
Dividing both sides by 2:
\[ 16 = 12 + B \]
Now, subtract 12 from both sides to find B:
\[ B = 16 - 12 = 4 \text{ meters} \]

5. **Calculating the Area**:
The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 12 \times 4 = 48 \text{ square meters} \]

### Final Answers:
- Length (L) = 12 meters
- Breadth (B) = 4 meters
- Area (A) = 48 square meters