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Nonlinear functions SAT question
Math · Advanced Math · Hard · Answer it here, explanation included.
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?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
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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