Question 190577: I'm having problems trying to figure out a problem, keep getting confused trying to figure it out. A picture frame is 20cm by 12cm. There are 84cm2 of picture showing. Find the width of the area not covered by the picture, assuming the picture is the same shape as the frame and is centered on the frame.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! if the picture is the same shape as the frame (geometrically "similar"),
then the ratio of length to width is 20:12 or 5:3
to find the width of the picture ___ 5k * 3k = 84
15k^2 = 84
k^2 = 5.6
so the width of the picture is 3sqrt(5.6)
the width of the uncovered frame would be ___ 12-[3sqrt(5.6)]
a more common problem is finding the width of the uncovered frame, assuming the width is uniform all the way around
let w=width of frame
(20 - 2w)(12 - 2w) = 84
FOILing ___ 240 - 64w + 4w^2 = 84
subtracting 84, dividing by 4, and rearranging ___ w^2 - 16w + 39 = 0
factoring ___ (w - 13)(w - 3) = 0
so w equals 13 or 3
since the total width of the frame is 12, the 13 is NOT realistic
so a frame border of uniform width is 3cm wide
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