A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is 13 feet long what are the dimensions of the garden

1. Write the equation for the Pythagorean theorem:
w^2 + (w + 7)^2 = 13^2

2. Calculate the square of 13:
13^2 = 169

3. Expand the equation:
w^2 + (w + 7)^2 = 169

w^2 + (w^2 + 14w + 49) = 169

4. Combine like terms:
2w^2 + 14w + 49 = 169

5. Simplify and rearrange the equation:
2w^2 + 14w + 49 - 169 = 0

2w^2 + 14w - 120 = 0

6. Divide the entire equation by 2 to simplify:
w^2 + 7w - 60 = 0

7. Factor the quadratic equation:
(w + 12)(w - 5) = 0

8. Solve for w:
- Either w + 12 = 0 which gives w = -12 (not possible in this context, since width can't be negative)
- Or w - 5 = 0 which gives w = 5

9. Find the length:
- Length = w + 7 = 5 + 7 = 12

Therefore, the width is 5 feet and the length is 12 feet.