# A football field is 100 yards long and 50 yards wide. How do you find the length of a diagonal of the football field?

Feb 13, 2016

${100}^{2} + {50}^{2} = 12500$; $\sqrt{12500} = 111.80$ yards

#### Explanation:

A football field is a rectangle, so a diagonal line creates 2 right triangles. The formula for the length of the sides of a right triangle is a^2 + b^2 = c^2" For this problem, we know $a$ and $b$, so we just have to find $c$.

${100}^{2} + {50}^{2} = {c}^{2} = 12500$

The length of the diagonal is $\sqrt{12500}$, which is 111.80 yards.

Feb 13, 2016

∼112 yards

#### Explanation:

Pythagorean Theorem: the diagonal of the football field is the hypotenuse. Let´s say the diagonal is C and the two other sides are A and B.

Width = A
Length = B
Diagonal = C

so: ${a}^{2} + {b}^{2} = {c}^{2}$

${50}^{2} + {100}^{2} = {c}^{2}$
$2500 + 10000 = {c}^{2}$
$12500 = {c}^{2}$
$c = \sqrt{12500}$

$c = 111.80$ yards