SOLUTION: Please help me solve: A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame.
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-> SOLUTION: Please help me solve: A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of the frame equals the area of the photograph. Find the width of the frame.
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You can put this solution on YOUR website! A 5 in. by 7 in. photograph is surrounded by a frame of uniform width.
The area of the frame equals the area of the photograph. Find the width of the frame.
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Let x = the width of the frame.
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Draw a rough sketch of this, label the picture dimensions, and width of the frame as x. Note that the dimensions of the frame will be: (7+2x) by (5+2x)
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Area of the picture: 5*7 = 35 sq in
Area of the frame given as the same, frame = 35 sq in also
Therefore the total area (picture & frame) will be 70 sq in
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A simple are equation:
(7+2x) * (5+2x) = 70
FOIL
35 + 14x + 10x + 4x^2 = 70
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4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
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4x^2 + 24x - 35 = 0
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Unfortunately this will not factor easily, have to resort to the quad equation:
a = 4; b = 24; c = -35
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: ; only worry about the positive solution here
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x =
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x = 1.213 inches is the width of the frame
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Check our solution
(7 + 2(1.213)) * (5 + 2(1.213))
(7+2.426) * (5+2.426)
9.426 * 7.426 = 69.997 ~ 70
