SOLUTION: A picture frame is 20 cm by 12 cm. There are 84 cm^2 of picture showing. Find the width of the area not covered by the picture, assuming the picture is the same shape as the frame

Question 1069801: A picture frame is 20 cm by 12 cm. There are 84 cm^2 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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
picture frame is 20 cm by 12 cm. There are 84 cm^2 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.
:
let x = the width of the frame (the width of the area not covered by the picture)
then the dimensions of the picture will be
(20-2x) by (12-2x)
the area of the picture
(20-2x)*(12-2x) = 84
FOIL
240 - 40x - 24x + 4x^2 = 84
combine to form a quadratic equation
4x^2 - 64x + 240 - 84 = 0
4x^2 - 64x + 156 = 0
simplify, divide by 4
x^2 - 16x + 39 = 0
You can use the quadratic formula; a=1; b=-16; c=39; but this will factor to:
(x-3)(x-13) = 0
x = 3 inches is the reasonable answer for the width of the frame
:
:
See if that checks out, find the area of the picture.
(20-6)*12-6) = 84
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