SOLUTION: A 9-by-12 rectangular picture is framed by a border of uniform width. Given that the combined area of picture plus frame is 180 square units, find the width of the border
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Question 230288: A 9-by-12 rectangular picture is framed by a border of uniform width. Given that the combined area of picture plus frame is 180 square units, find the width of the border Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! LET X BE THE BORDER WIDTH.
(9+2X)(12+2X)=180
108+24X+18X+4X^2=180
4X^2+42X+108-180=0
4X^2+42-72=0
(2X-3)(2X+24)=0
2X=3
X=3/2
X=1.5 ANS.
PROOF:
(9+2*1.5)(12+2*1.5)=180
(9+3)(12+3)=180
12*15=180
180=180
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