Question

1. a soccer field is 100 yards long and 50 yards wide. what is the diagonal distance across the field?

a. 111.8 yards
b. 125 yards
c. 110 yards
d. 120 yards

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a = 100$ yards (length), $b = 50$ yards (width), and $c$ is the diagonal. So $c=\sqrt{a^{2}+b^{2}}=\sqrt{100^{2}+50^{2}}$.

Step2: Calculate the squares

$100^{2}=10000$ and $50^{2}=2500$. Then $a^{2}+b^{2}=10000 + 2500=12500$.

Step3: Find the square - root

$c=\sqrt{12500}=111.803\approx111.8$ yards.

Answer:

A. 111.8 yards