Question 269559
Let {{{w}}} = width of border in ft
The area of the garden is:
{{{20*100 = 2000}}} ft2
The area of the garden + border is:
{{{(20+w)*(100 + w)}}}
{{{2000 + 100w + 20w + w^2}}}
The area of the border is (garden + border) - garden
{{{100 = 2000 + 100w + 20w + w^2 - 2000}}}
{{{w^2 + 120w = 100}}}
Solve by completing the square
{{{w^2 + 120w + (120/2)^2 = 100 + (120/2)^2}}}
{{{w^2 + 120w + 3600 = 3700}}}
{{{(w + 60)^2 = 3700}}}
Take the square root of both sides
{{{w + 60 = 60.828}}}
{{{w = .828}}} ft
{{{w = .828*12}}} in
{{{w = 9.93}}}
The width of the border is 9.93 inches
check:
The area of the garden + border is:
{{{(20+w)*(100 + w)}}}
{{{(20 + .828)*(100 + .828)}}}
{{{20.828*100.828 = 2100.04}}}
This is area of garden, 2000 ft2, plus 100 ft2 for border
OK