Question

A 10ft by 20ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft^2 , how wide is the walkway?

Answer 1

check the picture below.

so, we know the dimensions of the pool, is a 20x10, so its area is simply 200 ft², and we know the walkway is 216 ft², so the whole thing, including pool and walkway is really 200 + 216 ft².

now, as you see in the picture, the dimensions for the combined area is 20+2x and 10+2x, since the walkway is "x" long, therefore,

$\bf \stackrel{length}{(20+2x)}\stackrel{width}{(10+2x)}=200+216\implies \stackrel{FOIL}{4x^2+60x+200}=200+216 \\\\\\ 4x^2+60x=216\implies \stackrel{dividing~by~4}{x^2+15x=54} \\\\\\ x^2+15x-54=0\implies (x+18)(x-3)=0\implies x= \begin{cases} -18\\ \boxed{3} \end{cases}$

notice, it cannot be -18, since is a positive length unit.

Answer 2

Answer:

5

Step-by-step explanation: