I tried this with an area of $157m^2$ but got the wrong answer of $0.7334m$ when the correct answer was $1.138m$. Now I'm trying it with $140m^2$ I wanted to know what might be the issue with my steps below?
A garden plot must have a central planting area of length $13m$ and width $8m$. There is to be a sidewalk around its edge of width $w$. If the total area, planting area plus sidewalk area, is $140m^2$, what is the sidewalk width $w$ in meters?
$(13 + 2w)(8 + 2w) = 140$ $4w^2 + 42w + 104 = 140$ $4w^2 + 42w - 36 = 0$ We need to use the quadratic fomula to find the answer. ${x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$ $(2w + 0.79669)(2w - 11.29669) = 0$ $2w = 11.29669$ $w = \frac{11.29669}{2}$ $w$ can only be positive so we end up with $5.648345$