Answer:
- 4x^2 +44x = 48
- No, it is not reasonable
Step-by-step explanation:
If x is the width of the border, it adds 2x to each food listing dimension. The overall area of the menu and border will be ...
total area = (13+2x)(9+2x) = 4x^2 +44x +117
The area of the food listing is ...
food listing area = (13)(9) = 117 . . . . square inches
So, the border area is the difference of these:
border area = total area - food listing area
border area = (4x^2 +44x +117) - (117)
border area = 4x^2 +44x
We want this to be 48 square inches, so a suitable model is ...
4x^2 +44x = 48
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It is not reasonable for the border to be 2.5 inches wide.
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<em>Why 2.5 inches is not reasonable</em>
Dividing by 4 the equation becomes ...
x(x +11) = 12
One of the solutions is x=1. Using the value 2.5 for x would give ...
2.5(13.5) = 12 . . . . . false
