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

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Sigrid

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119 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

:
- 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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