Question 1056062
Let the width of the walkway = {{{ x }}}
My equation for the area of walkway is:
{{{ 2x*15 + 2x*( 20 + 2x ) = 200 }}}
{{{ 30x + 40x + 4x^2 = 200 }}}
{{{ 4x^2 + 70x - 200 = 0 }}}
{{{ 2x^2 + 35x - 100 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2-4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = 35 }}}
{{{ c = -100 }}}
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{{{ x = (-35 +- sqrt( 35^2-4*2*(-100) )) / (2*2) }}}
{{{ x = (-35 +- sqrt( 1225 + 800 )) / 4 }}}
{{{ x = ( -35 + sqrt( 2025 ) ) / 4 }}}
{{{ x = ( -35 + 45 ) / 4 }}}
{{{ x = 10/4 }}}
{{{ x = 5/2 }}}
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The width of the walkway is 2.5 ft
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check:
{{{ 4x^2 + 70x - 200 = 0 }}}
{{{ 4*2.5^2 + 70*2.5 - 200 = 0 }}}
{{{ 4*6.25 + 175 - 200 = 0 }}}
{{{ 25 + 175 - 200 = 0 }}}
{{{ 200 - 200 = 0 }}}
OK