QuESTION to A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across the field. How far do the pleyers run? 125 meters 175 meters 200 meters 150 meters

To find the diagonal distance players must run across the soccer field, we can use the Pythagorean theorem. The width and length of the field form a right triangle, where the width is one leg (90 meters), and the length is the other leg (120 meters). The formula is: \[ c = \sqrt{a^2 + b^2} \] Here, \(a = 90\) and \(b = 120\). Plugging in the values gives us: \[ c = \sqrt{90^2 + 120^2} = \sqrt{8100 + 14400} = \sqrt{22500} = 150 \text{ meters}. \] So the players run 150 meters! In a historical context, soccer fields have evolved in dimensions over the years, but the rectangle shape has remained. The standard size ensures fairness and uniformity across professional matches worldwide, contributing to the charm of the game that fans adore. When it comes to real-world applications, understanding distances like these is essential not just in sports but in various fields such as architecture and engineering. For example, if you're designing a playing field, knowing the diagonal distance helps in planning the placement of benches, goalposts, or even fencing around the field for safety.