Question

a soccer field is a rectangle 90 meters wide and 120 meters long. the coach asks players to run from one corner to the other corner diagonally across. what is this distance?

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the length and width of the rectangle are the two legs, and the diagonal is the hypotenuse. We can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 90\) meters (width) and \(b = 120\) meters (length).

Step2: Apply the Pythagorean theorem

First, calculate \(a^2\) and \(b^2\):
\(a^2 = 90^2 = 8100\)
\(b^2 = 120^2 = 14400\)

Then, find the sum of these squares:
\(a^2 + b^2 = 8100 + 14400 = 22500\)

Finally, take the square root of the sum to find the hypotenuse (diagonal):
\(c = \sqrt{22500} = 150\)

Answer:

The distance is 150 meters.