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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

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Answer to a math question 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

Expert avatar
Sigrid
4.5
120 Answers
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.

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