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Anonymous Posted on Feb 16, 2011

You are framing a rectangular print that is 10 inches wide and 34 inches long. this wall space has an area of 640 square inches. what is the width of the frame so that the framed print fits perfectly in this location?

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gdcroft

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  • Posted on Feb 23, 2011
gdcroft
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If we assume the width of the frame is X. Then the one dimension of the framed picture will be 2X + 20 and the other dimension of the picture will be 2X + 34. We know the total area of the framed picture should be 640 in^2. Therefore:
(2X + 10) * (2X + 34) = 640
If you multiply this out you get:
4X^2 + 88X + 340 = 640
Subtract 640 from both sides:
4X^2 + 88X - 300 = 0
Divide both sides by 4:
X^2 + 22X - 75 = 0
Use the quadratic equation to solve for X, with A=1, B=22, C=75
X = [-22 +/- sqr(22^2-4*(-75)] /2
This reduces to:
(-22 +/- 48) / 2
The negative solution doesn't make sense in this case. Therefore: X = (-22 + 28) /2 = 6/3 = 3

Therefore the width of the frame should be 3 inches.

  • gdcroft Feb 23, 2011

    I made a typo. The one dimension of the framed picture will be 2x 10 not 2X 20. The calculation and the answer are still correct.

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