Question 518189
the area of the pool is
{{{ 6*10 = 60 }}} m2
Let {{{x}}} = the width of the path
Both the length and width are increased by {{{2x}}}
The area of the path + pool = {{{ 120 }}} m2
{{{ (6 + 2x)*(10 + 2x) = 120 }}}
{{{ 60 + 20x + 12x + 4x^2 = 120 }}}
{{{ 4x^2 + 32x = 60 }}}
{{{ x^2 + 8x = 15 }}}
Complete the square
{{{ x^2 + 8x + (8/2)^2 = 15 + (8/2)^2
{{{ x^2 + 8x + 16 = 31 }}}
{{{ ( x + 4)^2 = 31 }}}
{{{ x + 4 = sqrt(31) }}}
{{{ x = sqrt(31) - 4 }}}
{{{ x = 5.5678 - 4 }}}
{{{ x = 1.5678 }}}
The width of the path is 1.5678 m
check answer:
{{{ (6 + 2x)*(10 + 2x) = 120 }}}
{{{ (6 + 2*1.5678)*(10 + 2*1.5678) = 120 }}}
{{{ (6 + 3.1356)*(10 + 3.1356) = 120 }}} 
{{{ 9.1356*13.1356 = 120 }}}
{{{ 120.0016 = 120 }}}
close enough