If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter sides?

Answer

To solve the problem step by step, we will use the formulas for the perimeter and area of a rectangle.

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the length of the shorter side of a rectangular flower bed, given its perimeter and area.

2. **Write the Formulas**:
- The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(l + b) \]
where \( l \) is the length and \( b \) is the breadth.
- The formula for the area \( A \) of a rectangle is:
\[ A = l \times b \]

3. **Set Up the Equations**:
- Given that the perimeter is 30 feet:
\[ 2(l + b) = 30 \]
Dividing both sides by 2:
\[ l + b = 15 \quad \text{(Equation 1)} \]
- Given that the area is 44 square feet:
\[ l \times b = 44 \quad \text{(Equation 2)} \]

4. **Express One Variable in Terms of the Other**:
- From Equation 1, we can express \( l \) in terms of \( b \):
\[ l = 15 - b \]

5. **Substitute into the Area Equation**:
- Substitute \( l \) in Equation 2:
\[ (15 - b) \times b = 44 \]
Expanding this gives:
\[ 15b - b^2 = 44 \]
Rearranging it to standard quadratic form:
\[ b^2 - 15b + 44 = 0 \quad \text{(Equation 3)} \]

6. **Factor the Quadratic Equation**:
- We need to factor Equation 3. We look for two numbers that multiply to 44 and add to -15. The numbers are -11 and -4:
\[ (b - 11)(b - 4) = 0 \]

7. **Solve for \( b \)**:
- Setting each factor to zero gives:
\[ b - 11 = 0 \quad \Rightarrow \quad b = 11 \]
\[ b - 4 = 0 \quad \Rightarrow \quad b = 4 \]

8. **Find Corresponding Lengths**:
- If \( b = 11 \), then:
\[ l = 15 - 11 = 4 \]
- If \( b = 4 \), then:
\[ l = 15 - 4 = 11 \]

9. **Identify the Shorter Side**:
- The lengths are 11 feet and 4 feet. Therefore, the length of the shorter side is:
\[ \text{Shorter side} = 4 \text{ feet} \]

### Final Answer:
The length of each of its shorter sides is **4 feet**.