Question #58dcc59f - SAT Suite Question Bank

ID: 58dcc59f

Modded SAT Question Bank by Abdullah Mallik

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?

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Correct Answer:

Rationale

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 $w plus 5$ feet. Thus the area of the garden will be $w times, open parenthesis, w plus 5, close parenthesis$ . It is also given that the area of the garden will be 104 square feet. Therefore, $w times, open parenthesis, w plus 5, close parenthesis, equals 104$ , which is equivalent to $w squared, plus 5 w, minus 104, equals 0$ . Factoring this equation results in $open parenthesis, w plus 13, close parenthesis, times, open parenthesis, w minus 8, close parenthesis, equals 0$ . Therefore, $w equals 8$ and $w equals negative 13$ . Because width cannot be negative, the width of the garden must be 8 feet. This means the length of the garden must be $8 plus 5, equals 13$ feet.

Question Difficulty: Hard