Rectangles ABCD and EFGH are similar. The length of each side of EFGH is 6 times the length of the

Question

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 ?

Accepted Answer

Choice D is correct. The area of a rectangle is given by b h , 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 b h yields x y . Therefore, the area, in square units, of ABCD can be represented by the expression x y . It&rsquo;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 6 x , and its height, in units, can be represented by the expression 6 y . Substituting 6 x for b and 6 y for h in the formula b h yields 6 x 6 y , which is equivalent to 36 x y . Therefore, the area, in square units, of EFGH can be represented by the expression 36 x y . It&rsquo;s given that the area of ABCD is 54 square units. Since x y represents the area, in square units, of ABCD , substituting 54 for x y in the expression 36 x y 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 .

Question 25288d