Question

1. a soccer field is a rectangle 80 meters wide and 105 meters long. the coach asks players to run from one corner to the other corner diagonally across the field. how far do the players run? draw a picture and then determine how far the players run. round to the nearest tenth.

picture:
the players will run _

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 80\), \(b=105\) and \(c\) is the length of the diagonal.
Substitute the values into the formula: \(80^{2}+105^{2}=c^{2}\).
Calculate \(80^{2}=6400\) and \(105^{2}=11025\).
Then \(6400 + 11025=c^{2}\), so \(c^{2}=17425\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{17425}\).
\(c\approx132.0\)

Answer:

\(132.0\) meters