Question 1155872
Let {{{ w }}} = the width of the walkway
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{{{ ( 40 - 2w )*( 35 - 2w ) = 1000 }}}
{{{ 1400 - 70w - 80w + 4w^2 = 1000 }}}
{{{ 4w^2 - 150w + 400 = 0 }}}
{{{ 2w^2 - 75w + 200 = 0 }}}
{{{ w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = -75 }}}
{{{ c = 200 }}}
{{{ w = (-(-75) +- sqrt( (-75)^2-4*2*200 ))/(2*2) }}}
{{{ w = ( 75 +- sqrt( 5625 - 1600 )) / 4 }}}
{{{ w = ( 75 +- sqrt( 4025 )) / 4 }}}
{{{ w = ( 75 - 63.4429) / 4 }}}
{{{ w = 11.5571 / 4 }}}
{{{ w = 2.889 }}}
the width is 2.89 ft, rounded off.
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check:
{{{ 2w^2 - 75w + 200 = 0 }}}
{{{ 2*2.889^2 - 75*2.889 + 200 = 0 }}}
{{{ 2*8.346321 - 216.675 + 200 = 0 }}}
{{{ 16.692642 - 216.675 + 200 = 0 }}}
{{{ 692642 - .675 = -.0176 }}}
I think the error is due to rounding off
You can verify this.
Get a 2nd opinion, too, if needed