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 corner diagonally across. what is this distance?
\boxed{} meters

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the diagonal of the rectangle is the hypotenuse. The width and length of the rectangle are the two legs of the right triangle. 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 \(b^{2}\):
\(a^{2}=90^{2}=90\times90 = 8100\)
\(b^{2}=120^{2}=120\times120 = 14400\)

Then, find the sum of \(a^{2}\) and \(b^{2}\):
\(a^{2}+b^{2}=8100 + 14400=22500\)

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

Answer:

150