Question

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

Answer 1

`100^2 + 50^2 = 12500`; `sqrt12500 = 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 `sqrt12500`, which is 111.80 yards.

Answer 2

∼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=sqrt12500`

`c= 111.80` yards