Rectangles ABCD and EFGH are similar. The length of each side of EFGH is 6 times the length of the corresponding side of ABCD. The area of ABCD is 54 square units. What is the area, in square units, of EFGH?

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Accepted Answer

Choice D is correct. The area of a rectangle is given by bh, where b is the length of the base of the rectangle and h is its height. Let x represent the length, in units, of the base of rectangle ABCD, and let y represent its height, in units. Substituting x for b and y for h in the formula bh yields xy. Therefore, the area, in square units, of ABCD can be represented by the expression xy. It’s given that the length of each side of EFGH is 6 times the length of the corresponding side of ABCD. Therefore, the length, in units, of the base of EFGH can be represented by the expression 6x, and its height, in units, can be represented by the expression 6y. Substituting 6x for b and 6y for h in the formula bh yields (6x)(6y), which is equivalent to 36xy. Therefore, the area, in square units, of EFGH can be represented by the expression 36xy. It’s given that the area of ABCD is 54 square units. Since xy represents the area, in square units, of ABCD, substituting 54 for xy in the expression 36xy yields 36(54), or 1,944. Therefore, the area, in square units, of EFGH is 1,944. Choice A is incorrect. This is the area of a rectangle where the length of each side of the rectangle is 1 ⁄ 6 , not 6, times the length of the corresponding side of ABCD. Choice B is incorrect. This is the area of a rectangle where the length of each side of the rectangle is 2 ⁄ 3 , not 6, times the length of the corresponding side of ABCD. Choice C is incorrect. This is the area of a rectangle where the length of each side of the rectangle is √ 6 , not 6, times the length of the corresponding side of ABCD.

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