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Question 140236This question is from textbook
: A oicture frame measures 12cm by 20cm. 84cm(squared) of picture shows inside the frame. Find the width of frame
This question is from textbook
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A picture frame measures 12 cm by 20 cm. 84 cm(squared) of picture shows inside the frame. Find the width of frame
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Let x = width of the frame
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then the dimension of the picture would be: (20-2x) by (12-2x)
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The area of the picture:
(20-2x)*(12-2x) = 84
FOIL
240 - 40x - 24x + 4x^2 = 84
Arrange as a quadratic equation:
4x^2 - 64x + 240 - 84 = 0
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4x^2 - 64x + 156 = 0
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Simplify, divide by 4:
x^2 - 16x + 39 = 0
Factor
(x-13)(x-3) = 0
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Two solutions, however,
x = +3 cm; is the only one that makes sense.
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Width of the frame: 12 - 2(3) = 6 cm
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Check solution by finding the area using the picture dimensions: L = 20-2(3) = 14
14 * 6 = 84 sq/cm as given
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did I make sense to you here? Let me know, please.
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