SOLUTION: A photo is 4 inches longer than it is wide. A 3inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions? Nam

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Question 191705This question is from textbook
: A photo is 4 inches longer than it is wide. A 3inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions? Name the variable in the equation. Thank you! This question is from textbook

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let x represent the width of the photo.

Then 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 and

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



Add -165 to each side:



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
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