SOLUTION: A rectangular picture measures 8” by 11” before it is framed. The frame has a uniform width, and the total area of the picture and the frame is 238 square inches. What is the widt

Algebra ->  Algebra  -> Rectangles -> SOLUTION: A rectangular picture measures 8” by 11” before it is framed. The frame has a uniform width, and the total area of the picture and the frame is 238 square inches. What is the widt      Log On

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Question 1891: A rectangular picture measures 8” by 11” before it is framed. The frame has a uniform width, and the total area of the picture and the frame is 238 square inches. What is the width of the frame?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the frame be x inches
the picture is 8x11, so its area is 88 square inches.
the picture and frame combined is (8+2x)*(11+2x), which equals an area of 238 square inches.
So lets expand this equation and see what it gives...
88+%2B+16x+%2B+22x+%2B+4x%5E2+=+238
4x%5E2+%2B+38x+%2B+88+=+238
4x%5E2+%2B+38x+-+150+=+0
2x%5E2+%2B+19x+-+75+=+0
%282x%2B25%29%28x-3%29+=+0
hence 2x+25=0 or x-3=0
ignore the first, since this is a negative value. Answer is x=3
cheers
Jon