The diagonal of the floor of a rectangular closet is 7.5 ft. The shorter side of the closet is 4.5 ft.
What is the area of the closet in square feet?
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A.
37 ft2
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B.
27 ft2
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C.
5.25 ft2
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D.
13.5 ft2
Correct Answer:
B. 27 ft2
Explanation:
To find the area of the rectangular closet, we first determine the length of the unknown side using the Pythagorean theorem, where the diagonal (7.5 ft) is the hypotenuse and one side is 4.5 ft. Squaring the diagonal gives 56.25 and squaring the known side gives 20.25. Subtracting these values results in 36, and taking the square root reveals the longer side is 6 ft. Finally, multiplying the length (6 ft) by the width (4.5 ft) results in an area of 27 square feet.
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