We can use the Pythagorean theorem to find the length of the diagonal. Let's call the width of the field a and the length b.
So, a = 90 meters and b = 120 meters.
The Pythagorean theorem states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse. In this case, the diagonal is the hypotenuse.
Using the Pythagorean theorem:
Diagonal^2 = Width^2 + Length^2
Diagonal^2 = (90)^2 + (120)^2
Diagonal^2 = 8100 + 14400
Diagonal^2 = 22500
Diagonal = √22500
Diagonal ≈ 150 meters
Therefore, the players ran approximately 150 meters.