a soccer field is a rectangle 90 meters wide and 120 meters long. The soccer team ran from one corner to the other corner, along the diagonal of the soccer field.
How far, in meters, did the players run?
To find the distance the players ran along the diagonal of the soccer field, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width of the field (90 meters) and the length of the field (120 meters) form two sides of a right triangle, and the diagonal of the field is the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
Diagonal² = Width² + Length²
Diagonal² = 90² + 120²
Diagonal² = 8100 + 14400
Diagonal² = 22500
Taking the square root of both sides, we find:
Diagonal ≈ √22500
Diagonal ≈ 150
Therefore, the players ran approximately 150 meters along the diagonal of the soccer field.