To find the distance between opposite corners of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side).
In this case, the gymnasium is a rectangle, so we can use the Pythagorean theorem to find the distance between opposite corners:
a = 30 meters (length of the rectangle)
b = 16 meters (width of the rectangle)
c = ? (distance between opposite corners)
c² = a² + b²
c² = (30 meters)² + (16 meters)²
c² = 900 + 256
c² = 1156
Taking the square root of both sides to solve for c:
c = √1156
c = 34
Therefore, the distance between opposite corners of the gymnasium is approximately 34 meters.