Question 191705
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Let <i><b>x</b></i> represent the width of the photo.


Then *[tex \LARGE x + 4] must be the length of the photo.


If the border is 3 inches wide all the way around, you must add 6 to the width (3 inches on each side) and 6 to the length (3 inches on the top and 3 on the bottom), so the outside dimensions of the border must be *[tex \LARGE x + 6] and *[tex \LARGE x + 10]


The total area is the product of the outside dimensions, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x + 6)(x + 10) = x^2 + 16x + 60 = 165]


Add -165 to each side:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + 16x - 105 = 0]


Factor and solve for x.


Exclude any negative root because we are looking for a positive measure of length.  The positive root will be the smaller dimension of the photo.  Add 4 to get the larger dimension of the photo.  Add 6 to each of those numbers to get the outer dimensions of the border.


Finally, find the product of the outer dimensions to verify that the overall area is actually 165 as a check on your work.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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