Final answer:
The length of the rectangular gymnasium is 2 feet.
Step-by-step explanation:
To find the length of the rectangular gymnasium, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the width is given as 5x feet. The area is given as (5x+5x) square feet. Simplifying (5x+5x), we get 10x. To find the length, we divide the area (10x) by the width (5x). This gives us a length of 2 feet.