Question 615076
The area of the swimming pool is {{{ 8*10 = 80 }}} m2
The area of the walkway is {{{ 72 }}} m2
The total area is {{{ 80 + 72 = 152 }}} m2
Let the width of the sidewalk = {{{ x }}}
The combined width is {{{ 8 + 2x }}} m
The combined length is {{{ 10 + 2x }}} m
Now I can say
{{{ ( 8 + 2x )*( 10 + 2x ) = 152 }}}
{{{ 4*( 4 + x )*( 5 + x ) = 152 }}}
{{{ 20 + 5x + 4x + x^2 = 38 }}}
{{{ x^2 + 9x - 18 = 0 }}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = 9 }}}
{{{ c = -18 }}}
{{{ x = (-9 +- sqrt( 9^2 - 4*1*(-18) )) / (2*1) }}} 
{{{ x = (-9 +- sqrt( 81 + 72 )) / 2 }}}
{{{ x = (-9 +- sqrt( 153 )) / 2 }}} 
{{{ x = (-9 + 12.37) / 2 }}} ( can't use the negative square root )
{{{ x =  3.37/2 }}}
{{{ x = 1.69 }}}
and
{{{ 2x + 8 = 3.38 + 8 }}}
{{{ 2x + 8 = 11.38 }}}
and
{{{ 2x + 10 = 3.38 + 10 }}}
{{{ 2x + 10 = 13.38 }}}
The width of the walkway is 1.69 m
The dimensions are 11.38 x 13.38 m2
check:
{{{ 11.38*13.38 = 152.26 }}}
{{{ 152.26 - 72 = 80.26 }}}
This looks close enough