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?
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.
(20 + 2 w)(22 + 2 w) = 1088 ... (10 + w)(11 + w) = 272

w^2 + 21 w - 162 = 0

factor to find w
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.
width of path ---- x metres

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

(22+2x)(20+2x) = 1088
the width of the path is 3

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