The area of a rectangular banner is 2,661 square inches. The banner's length x , in inches, is 24 inches

Question

The area of a rectangular banner is 2,661 square inches. The banner's length x , in inches, is 24 inches longer than its width, in inches. Which equation represents this situation?

Accepted Answer

Choice A is correct. It&rsquo;s given that the banner&rsquo;s length x , in inches, is 24 inches longer than its width, in inches. It follows that the banner&rsquo;s width, in inches, can be represented by the expression x - 24 . The area of a rectangle is the product of its length and its width. It's given that the area of the banner is 2,661 square inches, so it follows that 2,661 = x x - 24 , or 2,661 = x 2 - 24 x . Subtracting 2,661 from each side of this equation yields 0 = x 2 - 24 x - 2,661 . Therefore, the equation that represents this situation is 0 = x 2 - 24 x - 2,661 . Choice B is incorrect and may result from representing the width, in inches, of the banner as 24 - x , rather than x - 24 . Choice C is incorrect and may result from representing the width, in inches, of the banner as x + 24 , rather than x - 24 . Choice D is incorrect and may result from conceptual or calculation errors.

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