Question 579237
The area of the grass is {{{ 90*40 = 3600 }}} ft2
1/3 of the area is {{{ 1200 }}} ft2
If the border is of uniform width, and this width
is {{{ x }}}, then the total area minus the border is
{{{ (40 - 2x)*(90 - 2x) = 3600 - 1200 }}}
{{{ 3600 - 180x - 80x + 4x^2 = 2400 }}}
{{{ 4x^2 - 260x + 1200 = 0 }}}
{{{ x^2 - 65x + 300 = 0 }}}
Using quadratic formula:
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = -65 }}}
{{{ c = 300 }}}
{{{ x = (-(-65) +- sqrt( (-65)^2 - 4*1*300 ) ) / (2*1) }}}
{{{ x = ( 65 +- sqrt(  4225 -4*1*300 ))/(2*1) }}}
{{{ x = ( 65 +- sqrt(  4225 - 1200 ) ) / 2 }}}
{{{ x = ( 65 +- sqrt( 3025 ) ) / 2 }}}
{{{ x = ( 65 +- 55 ) / 2 }}}
{{{ x = 10/2 }}}
{{{ x = 5 }}}
and, with negative square root,
{{{ x = 120/2 }}}
{{{ x = 60 }}} ( not possible )
The border is 5 ft wide
check:
{{{ (40 - 2x)*(90 - 2x) = 3600 - 1200 }}}
{{{ (40 - 2*5)*(90 - 2*5) = 3600 - 1200 }}}
{{{ ( 40 - 10 )*( 90 - 10 ) = 3600 - 1200 }}}
{{{ 30*80 = 2400 }}}
{{{ 2400 = 2400 }}}
OK