Question

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).
A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to the cost of printing, the border should have an area of 48 square inches. The width of the border needs to be uniform around the entire menu. She has already determined that her food listings will fit within a 13-inch by 9-inch rectangular area.



The area of the decorative border can be modeled by the following equation, where x represents the width of the decorative border.

___x2 + ____ x = ____

Is it reasonable for the border to be 2.5 inches wide? ______(yes/no)

Answer 1

Answer:

$\displaystyle 4x^2 + 44 = 48$

Step-by-step explanation:

$\displaystyle [2x + 9][2x + 13] + 117 = 165 \\ \\ 4x^2 + 44x + 117 = 165 \\ \\ 4x^2 + 44x - 48 \\ [4x^2 + 48x] - [4x - 48] \\ 4x[x + 12] \: - 4[x + 12] \\ \\ [4x - 4][x + 12] \\ \\ -12, 1 = x$

Since we are talking about LENGTHS, we only want the NON-NEGATIVE root, which in this case is 1, therefore the border is one inch wide, so 2,5 inches is NOT reasonable.

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