Question 961186
Let {{{ x }}} = the extra length added to all
4 sides of the quilt
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One side will now measure {{{ 5 + 2x }}} ft
The other side will measure {{{ 4 + 2x }}} ft
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(a)
The extra area has to add up to {{{ 10 }}} ft2
I can say:
{{{ ( 5 + 2x )*( 4 + 2x ) - 4*5 = 10 }}}
{{{ 20 + 8x + 10x + 4x^2 - 20 = 10 }}}
{{{ 4x^2 + 18x - 10 = 0 }}}
{{{ 2x^2 + 9x - 5 = 0 }}}
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(b)
Use the quadratic formula
{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = 9 }}}
{{{ c = -5 }}}
{{{ x = ( -9 +- sqrt( 9^2 - 4*2*(-5) )) / (2*2) }}}
{{{ x = ( -9 +- sqrt( 81 + 40 )) / 4 }}}
{{{ x = ( -9 + 11 ) / 4 }}}
{{{ x = 2 / 4 }}}
{{{ x = .5 }}}
The width of the border is .5 ft
check:
{{{ ( 5 + 2x )*( 4 + 2x ) - 4*5 = 10 }}}
{{{ ( 5 + 2*.5 )*( 4 + 2*.5 ) - 4*5 = 10 }}}
{{{ ( 5 + 1 )*( 4 + 1 ) - 20 = 10 }}}
{{{ 6*5 - 20 = 10 }}}
{{{ 30 - 20 = 10 }}}
{{{ 10 = 10 }}}
OK
I had to assume a lot here, like the extra fabric
did not get folded, but I think I got what
they were after
Hope this helps