allegansveritatem
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- Jan 10, 2018
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132. A square page in a book measures 10 inches on each side. The printed matter on the page is to be surrounded by a blue margin of uniform width on all sides. The area of the blue margin is to be equal to the area of the portion of the page containing the printed matter. What are the dimensions of the portion of the page on which the print appears?
Here is how I set it up: 10^2 -(10-2x)^2= (10-2x)^2
Here is the answer: (I did this about 4 times by hand before using the calculator):
Solve [math]8c^2\, -\, 80c\, +\, 100\, =\, 0[/math] for [math]c[/math]
. . . . .[math]c\, =\, \dfrac{-5\,\left(\sqrt{2\,}\, -\, 2\right)}{2}\, \mbox{ or }\, c\, =\, \dfrac{5\, \left(\sqrt{2\,}\, +\, 2\right)}{2}[/math]
Here is the book's answer:
132. [math]5\, \sqrt{2\,}\, \mbox{in.}\, \times\, 5\, \sqrt{2\,}\, \mbox{in.; or }\, 7.1\, \mbox{in.}\, \times\, 7.1\, \mbox{in.}[/math]
My question is: Did the author or his representative do this problem the same way I did? I know my answer is right because it checks out.
Here is how I set it up: 10^2 -(10-2x)^2= (10-2x)^2
Here is the answer: (I did this about 4 times by hand before using the calculator):
Solve [math]8c^2\, -\, 80c\, +\, 100\, =\, 0[/math] for [math]c[/math]
. . . . .[math]c\, =\, \dfrac{-5\,\left(\sqrt{2\,}\, -\, 2\right)}{2}\, \mbox{ or }\, c\, =\, \dfrac{5\, \left(\sqrt{2\,}\, +\, 2\right)}{2}[/math]
Here is the book's answer:
132. [math]5\, \sqrt{2\,}\, \mbox{in.}\, \times\, 5\, \sqrt{2\,}\, \mbox{in.; or }\, 7.1\, \mbox{in.}\, \times\, 7.1\, \mbox{in.}[/math]
My question is: Did the author or his representative do this problem the same way I did? I know my answer is right because it checks out.
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