Question a-land
A landscaper is designing a rectangular . The length of the is to be 5 feet longer than the width. If the area of the will be 104 square feet, what will be the length, in feet, of the ?
A landscaper is designing a rectangular . The length of the is to be 5 feet
Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
The correct answer is 13. Let w represent the width of the rectangular , in feet. Since the length of the will be 5 feet longer than the width of the , the length of the will be 
feet. Thus the area of the will be 
. It is also given that the area of the 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 must be 8 feet. This means the length of the must be 
feet.
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