SOLUTION: A picture frame is 20 inches by 12 inches. There are 84inches^2 of the picture showing. Find the width of the frame. __

SOLUTION: A picture frame is 20 inches by 12 inches. There are 84inches^2 of the picture showing. Find the width of the frame. ___ inches Thanks

Question 41196: A picture frame is 20 inches by 12 inches. There are 84inches^2 of the picture showing. Find the width of the frame.
___ inches
Thanks
Found 2 solutions by fractalier, checkley71:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let the width of the frame be x. Let the dimensions of just the picture be L and W. Thus we know
A = LW = 84
We also know that
(L + 2x)(W + 2x) = 240
We also know that
L + 2x = 20
W + 2x = 12
Let us solve these for L and W and plug in to the first equation, so we get
L = 20 - 2x
W = 12 - 2x
and then
(20 - 2x)(12 - 2x) = 84
240 - 64x + 4x^2 = 84
4x^2 - 64x + 156 = 0
x^2 - 16x + 39 = 0
(x - 13)(x - 3) = 0
x = 13 or x = 3
but x cannot be 13, so
x = 3
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
20*12=240 thus (20-x)(12-x)=84 or 240-32x+x~2=84 or x~2-32x+156 or
(x-26)(x-6)=0 or x=26 & x=6 inch wide frame
proof (20-6)(12-6)=84 or 14*6=84 or 84=84
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