SOLUTION: A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame.
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Question 327240: A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame. Answer by solver91311(24713) (Show Source):
Let represent the width of the frame. Then the outside dimensions of the frame have to be and .
If the area of the frame is equal to the area of the picture, the area of the frame plus the picture has to be two times the area of the picture,
The overall area of the frame and the picture is the product of the outside dimensions of the frame, so:
Multiply the binomials using FOIL, collect like terms to put the quadratic in standard form, and solve. The quadratic DOES NOT factor so you will need to use the quadratic formula. Discard the negative root because you are looking for a positive measure of distance. Leave the answer in simplified radical form since no precision specification was given and therefore an exact answer requirement is implied.
