Question 87923
A picture 9 inches wide and 12 inches long is surrounded by a frame of uniform width.  The area of the frame only is 162 square inches.  Find the width of the frame.
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Draw the picture of the frame around the picture.
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Let the width of the frame be "x"inches.
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Area of picture with frame around is length*width
Width = 9 + 2x inches
length = 12 + 2x inches
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Larger area = (9+2x)(12+2x)
=2(9+2x)(6+x)
=2[54+21x+2x^2]
=4x^2 + 42x + 108
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Area of frame = larger area - 9*12
= 4x^2 + 42x +108 - 108
= 4x^2 + 42x
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Area of frame = 162 sq. in.
4x^2+42x= 162
2x^2 + 21x -81 = 0
x = [-21+33]/4 = 3 or x = [-21-33]/4 = -54/4 = -27/2
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Realistic Answer: width = 3 inches
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Cheers,
Stan H.