Question

Dillon ran the width of a field, a distance of 60 yards. Then he ran the length of the field, a distance of 80 yards. How far apart are opposite corners of the field?

yards

Answer 1

To find the distance between opposite corners of the field, we can use the Pythagorean theorem. The width and length of the field represent the two legs of a right triangle, where the distance between the opposite corners is the hypotenuse.

Given:
- Width (one leg) = 60 yards
- Length (another leg) = 80 yards

Let \( a = 60 \) yards, and \( b = 80 \) yards. According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Substituting the values:

\[
c^2 = 60^2 + 80^2
\]

Calculating \( 60^2 \) and \( 80^2 \):

\[
60^2 = 3600
\]
\[
80^2 = 6400
\]

Now, adding these:

\[
c^2 = 3600 + 6400 = 10000
\]

Taking the square root to find \( c \):

\[
c = \sqrt{10000} = 100
\]

Thus, the distance between the opposite corners of the field is

\[
\boxed{100} \text{ yards.}
\]