SOLUTION: Sally wants to put a border around a 4x6 inch picture. She would like the border to be twice the area of the picture. What is the border width should Sally use (in inches)?

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Question 883022: Sally wants to put a border around a 4x6 inch picture. She would like the border to be twice the
area of the picture. What is the border width should Sally use (in inches)?

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
ally wants to put a border around a 4x6 inch picture. She would like the border to be twice the
area of the picture. What is the border width should Sally use (in inches)?
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Draw the picture::
You have a rectangle inside a rectangle.
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The inner rectangle has area 4X6 = 24 in^2
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The ourter rectangle (including the inner) has area::
(6+2x)(4+2x) = 24 + 20x + 4x^2
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The frame area = outer - inner = 4x^2 + 20x.
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Equation:
4x^2 + 20x = 2*24
x^2 + 5x - 12 = 0
x = [-5 +- sqrt(25-4*-12)]/2 = (-5+sqrt(73))/2 = 1.77 inches)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The area of the picture is in2
Let = the width of the border
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Note that gets added to each
dimension when you add the border
all around
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The area of the picture plus the border is:

The area of the border is:

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Sally wants the area of the border to be
in2
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Divide both sides by

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You can complete the square:

Take the square root of both sides

The border width should be 1.772 in
check:

close enough
Hope I got it