Question

Seth has a garden with dimension 9 feet long x 8 feet wide. He wants to enlarge the garden to an area of 120 square feet. How much farther will he need to extend the length of the garden to attain his desired area?

Answer 1

To determine how much farther Seth needs to extend the length of his garden to reach an area of 120 square feet, we first need to calculate the current area of the garden and then find the required dimensions to achieve the desired area.

1. **Calculate the current area of the garden**:
\[
\text{Current area} = \text{length} \times \text{width} = 9 \, \text{feet} \times 8 \, \text{feet} = 72 \, \text{square feet}
\]

2. **Determine the desired increase in area**:
\[
\text{Desired area} = 120 \, \text{square feet}
\]
\[
\text{Additional area needed} = \text{Desired area} - \text{Current area} = 120 \, \text{square feet} - 72 \, \text{square feet} = 48 \, \text{square feet}
\]

3. **Find the new length while keeping the width the same**:
Let \( l \) be the new length of the garden. Seth wants to maintain the width of the garden, which is still 8 feet. The equation for the area will be:
\[
\text{Area} = \text{new length} \times \text{width} = l \times 8 \, \text{feet}
\]
Setting this equal to the desired area, we have:
\[
l \times 8 = 120
\]

4. **Solve for the new length \( l \)**:
\[
l = \frac{120}{8} = 15 \, \text{feet}
\]

5. **Calculate how much farther the length needs to be extended**:
The original length was 9 feet, and the new length required is 15 feet. Therefore, the extension needed is:
\[
\text{Extension} = \text{new length} - \text{original length} = 15 \, \text{feet} - 9 \, \text{feet} = 6 \, \text{feet}
\]

Thus, Seth needs to extend the length of the garden by **6 feet** to attain his desired area of 120 square feet.