SOLUTION: The page of a book measures 6in by 9in. A uniform border around the page leaves 28in^2 for type. What are the dimensions of the type area? I have no idea where to begin with thi

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Question 566994: The page of a book measures 6in by 9in. A uniform border around the page leaves 28in^2 for type. What are the dimensions of the type area?
I have no idea where to begin with this. How do I solve this?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The page of a book measures 6in by 9in. A uniform border around the page leaves 28in^2 for type. What are the dimensions of the type area?
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Draw the picture of a rectangle inside a rectangle.
The outer rectangle (including the inner triangle)
has area = 6*9 = 54 sq in.
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The dimensions of the inner rectangle are:
width = 6-2x
length = 9-2x
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Equation:
(6-2x)(9-2x) = 28
54 - 12x -18x + 4x^2 = 28
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4x^2 - 30x + 26 = 0
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2x^2 - 15x + 13 = 0
2x^2 - 13x - 2x + 13 = 0
x(2x-13)-(2x-13) = 0
(2x-13)(x-1) = 0
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Possible solutions:
x = 13/2 or x = 1
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Find Width and length:
width = 6-2x
length = 9-2x
---
If x = 1 you get:
width = 6-2x = 4
length = 9-2x = 7
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If x = (13/2) you get:
width = 6-2(13/2) is negative
length = 9-2(13/2) is negative
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So the only solution is width = 4 and length 7
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cheers,
Stan H.
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