Question 302419
I'm not familiar with the 5-step process, but I
can show you how I'd do it
Let {{{x}}} = the width of the border
The area of the garden is {{{6*15 = 90}}} yd2
The dimensions of the garden + border are:
{{{6 + 2x}}} by {{{15 + 2x}}}
The area of the garden + border is
{{{A = (6 + 2x)*(15 + 2x)}}}
The area of the garden is {{{6*15 = 90}}} yd2
The area of the border is {{{100}}} yd2
{{{A = 190}}}
{{{190 = (6 + 2x)*(15 + 2x)}}}
{{{190 = 90 + 30x + 12x + 4x^2}}}
{{{4x^2 + 42x - 100 = 0}}}
Solve using quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 4}}}
{{{b = 42}}}
{{{c = -100}}}
{{{x = (-42 +- sqrt( 42^2-4*4*(-100) ))/(2*4) }}}
{{{x = (-42 +- sqrt( 1764 + 1600 ))/8 }}}
{{{x = (-42 +- sqrt( 3364 ))/8 }}}
{{{x = (-42 + 58)/8}}} (there's another solution, but it's negative)
{{{x = 2}}}
The border around the garden is 2 yds wide
check:
{{{190 = (6 + 2x)*(15 + 2x)}}}
{{{190 = (6 + 4)*(15 + 4)}}}
{{{190 = 10*19}}}
{{{190 = 190}}}
OK