A garden plot must have a central planting area of length 13 m and width 8 m. There is to be a sidewalk around its edge of width w. If the total area, planting area plus sidewalk area, is 144 m^2, what is the sidewalk width w in meters?
[Math] Find width of a rectangle around a smaller rectangle
geometry
Best Answer
Hint: Draw a picture. You can see that the total region has length $13+2w$ and width $8+2w$. It follows that $$(2w+13)(2w+8)=144.$$ Now you can use general techniques: the equation, when you expand, is a nice quadratic equation. Solve, say by using the Quadratic Formula. There will be two solutions, but one is easily discarded.
Added: When you expand, you will get $4w^2+42w-40=0$.