A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?
Correct answer: 13 (parsed from the explanation — this source omits an answer key for this item)
Explanation
The correct answer is 13. Let w represent the width of the rectangular garden, in feet. Since the length of the garden will be 5 feet longer than the width of the garden, the length of the garden will be feet. Thus the area of the garden will be
. It is also given that the area of the garden will be 104 square feet. Therefore,
, which is equivalent to
. Factoring this equation results in
. Therefore,
and
. Because width cannot be negative, the width of the garden must be 8 feet. This means the length of the garden must be
feet.
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