To solve the problem from the image, we need to find the length and width of the rectangular garden.

Given:

• Perimeter of the rectangular garden = 30 feet.
• The length is 7 feet more than the width.

Formula for the perimeter of a rectangle:

$\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$ Let:

• $L$ be the length of the garden.
• $W$ be the width of the garden.

Step-by-step solution:

1. From the problem, we know $L = W + 7$ (since the length is 7 feet more than the width).

2. The perimeter formula is: $2 \times (L + W) = 30$

3. Substitute $L = W + 7$ into the equation: $2 \times ((W + 7) + W) = 30$

4. Simplify: $2 \times (2W + 7) = 30$ $4W + 14 = 30$

5. Subtract 14 from both sides: $4W = 16$

6. Divide by 4: $W = 4$ So, the width of the garden is 4 feet.

7. Now, substitute $W = 4$ back into $L = W + 7$: $L = 4 + 7 = 11$ So, the length of the garden is 11 feet.

Final answer:

• Length = 11 feet.
• Width = 4 feet.

Would you like further clarification or a breakdown of any specific step?

Related Questions:

1. How would the dimensions change if the perimeter were 40 feet but the same condition applied?
2. What if the length was 5 feet more than the width instead of 7 feet?
3. How can you solve for the area of the garden given the length and width?
4. How would the dimensions change if the perimeter were halved?
5. How can you express the length in terms of width algebraically for any perimeter?

Tip:

Always check your answers by plugging them back into the original formula to ensure they satisfy all conditions.