Question 286261
A of picture = 5*7=35
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Frame width = x
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The area of the frame = area of the picture, which means it is 35+35 = 70
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(2x+5)(2x+7) = 70
4x^2 +14x +10x + 35 = 70
4x^2 +24x + 35 = 70
4x^2 +24x -35 = 0
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Using the quadratic solver...
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*[invoke quadratic "x", 4, 24, -35 ]
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x = 1.2130  (The other root is negative, so it is spurious.)
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Checking, what is the area of a rectangle defined by the outside of the frame?
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(5+2(1.2130)) * (7 + 2(1.2130)) = (5+2.426)*(7+2.426) = 7.246*9.246 = 69.997,
which is pretty close to 70.
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Done.