The length of a rectangle is 50 inches and the width is x inches. The perimeter is at most 210

Question

The length of a rectangle is 50 inches and the width is x inches. The perimeter is at most 210 inches. Which inequality represents this situation?

Accepted Answer

Choice A is correct. The perimeter of a rectangle is equal to the sum of 2 times its length and 2 times its width. It's given that the rectangle's length is 50 inches and the width is x inches. Therefore, the perimeter, in inches, is 2 50 + 2 x , or 100 + 2 x , which is equivalent to 2 x + 100 . It's given that the perimeter is at most 210 inches; therefore, 2 x + 100 &#8804; 210 represents this situation. Choice B is incorrect. This inequality represents a situation where the perimeter is at least, rather than at most, 210 inches. Choice C is incorrect. This inequality represents a situation where 2 times the length, rather than the length, is 50 inches. Choice D is incorrect. This inequality represents a situation where 2 times the length, rather than the length, is 50 inches, and the perimeter is at least, rather than at most, 210 inches.

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