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Geometry and Trigonometry / Area and volume Difficulty: Medium

Square A has side lengths that are $246$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$ ?

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Explanation

Choice A is correct. The area of a square is $s^{2}$ , where $s$ is the side length of the square. Therefore, the area of square B is $b^{2}$ , where $b$ is the side length of square B. It’s given that square A has side lengths that are $246$ times the side lengths of square B. Therefore, the side length of square A can be represented by the expression $246 b$ . It follows that the area of square A is $left parenthesis 246 b right parenthesis squared$ , or $60,516 b squared$ . It’s given that the area of square A is $k$ times the area of square B, so $60,516 b squared equals k b squared$ . Therefore, the value of $k$ is $60,516$ .

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

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

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