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Geometry and Trigonometry / Area and volume Difficulty: Medium

Square X has a side length of $12$ centimeters. The perimeter of square Y is $2$ times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

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Explanation

Choice D is correct. The perimeter, $P$ , of a square can be found using the formula $upper P equals 4 s$ , where $s$ is the length of each side of the square. It's given that square X has a side length of $12$ centimeters. Substituting $12$ for $s$ in the formula for the perimeter of a square yields $upper P equals 4 left parenthesis 12 right parenthesis$ , or $upper P equals 48$ . Therefore, the perimeter of square X is $48$ centimeters. It’s also given that the perimeter of square Y is $2$ times the perimeter of square X. Therefore, the perimeter of square Y is $2 left parenthesis 48 right parenthesis$ , or $96$ , centimeters. Substituting $96$ for $P$ in the formula $upper P equals 4 s$ gives $96 equals 4 s$ . Dividing both sides of this equation by $4$ gives $24 equals s$ . Therefore, the length of one side of square Y is $24$ centimeters.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.