A pool measuring 20 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combine is 1088 square meters, what is the width of the path?

Question

A pool measuring 20 meters by 22 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combine is 1088 square​ meters, what is the width of the​ path?

oobleck · Answer

If the path has width w, then since the path is along both sides and both ends, the total area is
(20+2w)(22+2w) = 1088
Now just solve for w.

or, just ask, which two factors of 1088 differ by 2? Since they are so close together, they will both be close to √1088 ≈ 33. So, I'd try 32 and 34.

R_scott · Answer

(20 + 2 w)(22 + 2 w) = 1088 ... (10 + w)(11 + w) = 272 w^2 + 21 w - 162 = 0 factor to find w

Reiny · Answer

width of path ---- x metres

area of outer rectangle = (22+2x)(20+2x)

(22+2x)(20+2x) = 1088

expand, simplify and solve the resulting equation.
You will get two integer answers, make sure to reject the negative root.

bim bog · Answer

width of path ---- x metres area of outer rectangle = (22+2x)(20+2x) (22+2x)(20+2x) = 1088

marley · Answer

the width of the path is 3

A pool measuring 20 meters by 22 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combine is 1088 square​ meters, what is the width of the​ path?

A pool measuring 20 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combine is 1088 square meters, what is the width of the path?