A rectangular football field is 64 meters wide and 100 meters long. A player runs from one corner of the field in a diagonal line to the opposite corner.
How far did the player run?
Round your answer to the nearest meter.
We can use the Pythagorean theorem to solve this problem. Let's label one of the corners as A, the opposite corner as C, and the third corner (adjacent to both A and C) as B. Then, we have:
AB = 64 meters (since sides AB and CD are parallel and equal in length)
BC = 100 meters (since sides BC and AD are parallel and equal in length)
AC = ? (what we're trying to find)
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides, we have:
AC² = AB² + BC²
AC² = 64² + 100²
AC² = 4096 + 10000
AC² = 14096
AC ≈ √14096
AC ≈ 118.7 meters (rounded to the nearest meter)
Therefore, the player ran approximately 119 meters.