Question 883022
The area of the picture is {{{ 4*6 = 24 }}} in2
Let {{{ w }}} = the width of the border
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Note that {{{ 2w }}} 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:
{{{ ( 4 + 2w )*( 6 + 2w ) = 24 + 20w + 4w^2 }}}
The area of the border is:
{{{ ( 24 + 20w + 4w^2 ) - 24 = 4w^2 + 20w }}}
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Sally wants the area of the border to be
{{{ 2*4*6 = 48 }}} in2
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{{{ 4w^2 + 20w = 48 }}}
Divide both sides by {{{ 4 }}}
{{{ w^2 + 5w = 12 }}}
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You can complete the square:
{{{ w^2 + 5w + (5/2)^2 = 12 + (5/2)^2 }}}
{{{ w^2 + 5w + 25/4  = 48/4 + 25/4 }}}
{{{ ( w + 5/2 )^2 = 73/4 }}}
Take the square root of both sides
{{{ w + 5/2 = sqrt(73) / 2 }}}
{{{ w = ( sqrt(73) - 5 ) / 2 }}}
{{{ w = ( 8.544 - 5 ) / 2 }}}
{{{ w = 3.544/2 }}}
{{{ w = 1.772 }}}
The border width should be 1.772 in
check:
{{{ ( 4 + 2w )*( 6 + 2w ) - 24 = 2*4*6 }}}
{{{ ( 4 + 2w )*( 6 + 2w ) - 24 = 48 }}}
{{{ ( 4 + 3.544 )*( 6 + 3.544 ) - 24 = 48 }}}
{{{ 7.544*9.544 = 72 }}}
{{{ 71.9999 = 72 }}}
close enough
Hope I got it