Question

The length of a football field is 100 yards and the width is 53 yards. in the first game of the season, joe don catches the opening kickoff at the corner of the goal line and runs straight as a string the diagonal length of the field to score a touchdown. the next day, the local paper credits joe for a 100 yard touchdown run, but how far did he actually run?

Answer 1

Joe Don actually ran 113.2 yards

Explanation:

Length of the football field = 100 yd

Width of the football field = 53 yd

The football field is rectangular in shape. So in order to find the diagonal of the field, we need to split it up into two right triangles.

In one of the right triangles, the length and width becomes the two sides of it and diagonal is the third side.

In order to find the third side (diagonal), we need to apply the Pythagoras theorem.

So,

Diagonal² = 100² + 53²

Diagonal² = 10000 + 2809

Diagonal² = 12809

Taking square root on both sides

`\sqrt{Diagonal^(2) } =√(12809)`

Diagonal = 113.17 yd

Diagonal = 113.2 yd (approx)

Thus Joe Don actually ran 113.2 yards

Answer 2

By the Pythagorean theorem, the diagonal of a rectangle 53 yards by 100 yards is
.. diagonal = √((53 yd)^2 +(100 yd)^2) = (√12809) yd ≈ 113.2 yd

Joe Don's run was 113.2 yards.