Question

a rectangular field is 50 yards wide and 100 yards long. patrick walks diagonally across the field. how far does he walk?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 50\), \(b=100\), and \(c\) is the diagonal.

$$\begin{align*} c^{2}&=50^{2}+100^{2}\\ c^{2}&=2500 + 10000\\ c^{2}&=12500 \end{align*}$$

Step2: Solve for \(c\)

Take the square root of \(c^{2}\).

$$ c=\sqrt{12500}\approx111.8 $$

Answer:

\(111.8\) yards