Let x be the smaller even integer representing the width of the rectangle, then the length of the rectangle is x + 2 (since they are consecutive even integers).
The area of the rectangle is given by length × width, so we have:
Area = (x + 2) × x = 360
Expanding the expression on the left side, we get:
x^2 + 2x = 360
Rearranging, we get:
x^2 + 2x - 360 = 0
We can factor the left side of the equation as:
(x + 20) (x - 18) = 0
Thus, the solutions are x = -20 or x = 18. Since x represents the width, which cannot be negative, we have x = 18.
Therefore, the width of the rectangle is 18 meters and the length is x + 2 = 20 meters.