Question 190577
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