SOLUTION: Could you please help with the following problem: 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 i
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Question 87923This question is from textbook Introductory and Intermediate Algebra
: Could you please help with the following problem: 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.
Thank you very much for any help you can provide. This question is from textbook Introductory and Intermediate Algebra
You can put this solution on YOUR website! 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.
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