SOLUTION: A rectangular photo of dimensions 8 cm by 9 cm is placed in a picture frame of uniform width on all sides. The resulting total area (picture and frame) is 210 square cm. What is t

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Question 864308: A rectangular photo of dimensions 8 cm by 9 cm is placed in a picture frame of uniform width on all sides. The resulting total area (picture and frame) is 210 square cm.
What is the width of the picture frame?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
w for frame width

%288%2B2w%29%289%2B2w%29=210----Area calculation
2%2A2%284%2Bw%29%284.5%2Bw%29=210
2%28w%2B4%29%28w%2B4.5%29=105
%28w%2B4%29%282w%2B9%29=105
2w%5E2%2B17w%2B36=105
2w%5E2%2B17w-69=0
Probably factorable; checking;
discrim, 17^2-4*2(-69)=289+8*69=841=29*29
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highlight%28%282w%2B23%29%28w-3%29=0%29
The width that makes sense is highlight%28highlight%28w=3%29%29.