Question

The perimeter of a rectangular garden is 42 feet. The length of the garden is 1 foot more than three times its width. What is the length and width of the garden?(1 point)
Responses

The length is 31.75 feet and the width is 10.25 feet.
The length is 31.75 feet and the width is 10.25 feet.

The length is 14.33 feet and the width is 6.67 feet.
The length is 14.33 feet and the width is 6.67 feet.

The length is 16 feet and the width is 5 feet.
The length is 16 feet and the width is 5 feet.

The length is 12 feet and the width is 9 feet.
The length is 12 feet and the width is 9 feet.
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Answer 1

To solve for the dimensions of the rectangular garden, we can use the given information to set up a system of equations.

1. **Let \( w \) be the width of the garden.**
2. **Then the length \( l \) can be expressed as:**
\[
l = 3w + 1
\]

3. **The formula for the perimeter \( P \) of a rectangle is:**
\[
P = 2l + 2w
\]
Given that the perimeter is 42 feet:
\[
2l + 2w = 42
\]

4. **We can simplify this equation:**
\[
l + w = 21
\]

5. **Now we can substitute the expression for \( l \) from step 2 into this equation:**
\[
(3w + 1) + w = 21
\]

6. **Combine like terms:**
\[
4w + 1 = 21
\]

7. **Subtract 1 from both sides:**
\[
4w = 20
\]

8. **Now divide by 4:**
\[
w = 5
\]

9. **Use the width to find the length:**
\[
l = 3(5) + 1 = 15 + 1 = 16
\]

Thus, the dimensions of the garden are:
- **Length = 16 feet**
- **Width = 5 feet**

**Final answer:** The length is 16 feet and the width is 5 feet.