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?
$\endgroup$2 Answers
$\begingroup$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 $4w^2+42w-40=0$.
$\endgroup$ 3 $\begingroup$The length of the bigger rectangle is $13+2x$ meters and the width is $8 + 2x$ meters. We know the area and now we do a simle calculation:
$$(13 + 2x)(8 + 2x) = 144$$ $$104 + 16x + 26x + 4x^2 = 144$$ $$4x^2 + 42x = 40$$
We just need the positive solution which is:
$$x = \frac{\sqrt{601} - 21}{4}$$
$\endgroup$ 3
