Question

14/20
a rectangular field is 50 yards wide and 100 yards long. patrick walks diagonally across the field. how
far does he walk?
115 yards
111.8 yards
119 yards
127.3 yards

Explanation:

Step1: Apply the Pythagorean theorem

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

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(50^{2}=2500\), \(100^{2} = 10000\).
So, \(2500+10000=c^{2}\), which simplifies to \(c^{2}=12500\).

Step3: Solve for \(c\)

Take the square root of \(12500\), \(c=\sqrt{12500}\approx111.8\) (using a calculator, \(\sqrt{12500}=\sqrt{2500\times5}=50\sqrt{5}\approx50\times2.236 = 111.8\)).

Answer:

111.8 yards