Answer:
width = 2.5 feet
Step-by-step explanation:
Suzanne has a rectangular garden which is 18 feet long and 11 feet wide.
Area of the garden = length times width = 18 times 11= 198 square foot
Let 'w' be the width of the border
Length of the garden with border = 18+2w
Width of the garden with border = 11+2w
Area of the garden with border = [tex](18+2w)(11+2w)=4w^2+58w+198[/tex]
Area of the border = [tex]4w^2+58w+198-198=4w^2+58w[/tex]
She has 168 square foot of paving stones,
[tex]4w^2+58w=168[/tex]
Solve for w
apply quadratic formula
a= 4, b= 58 and c=-168
[tex]\quad x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]w=\frac{-58+-\sqrt{58^2-4\cdot \:4\left(-168\right)}}{2\cdot \:4}[/tex]
[tex]w=\frac{-58+-\sqrt{6052}}{8}[/tex]
we get two values for w
[tex]w=\frac{-58+\sqrt{6052}}{8}=2.47[/tex]
[tex]w=\frac{-58-\sqrt{6052}}{8}=-16.97[/tex]
