Question

The scene is a football field. Ben catches a kick and follows the path shown in the diagram. He starts at

the east end of one goal line (near the lower right of the diagram). He runs first to the 20-yard line on the
west sideline and then to the 50-yard line on the east sideline. Finally he runs for a touchdown at the west end of the other goal line. The field is 53.33 yards wide and 100 yards long. How far does Ben run altogether?

Answer 1

The distance he traveled in yards is 191.25 yards.

What is Pythagora's theorem?

Using Pythagorean theorem

Each of the diagonal/slant line makes right triangle with sides of the field

Let Li represents the slant lines

Let's evaluate each

L₁² = 20² + 53.33²

= 400 + 2844.09

L₁² = 3244.09

L₁ = √3244.09

= 56.96 yds

L₂² = 30² + 53.33²

= 900 + 2844.09

= 3744.09

L₂ = √3744.09

= 61.19 yds

L₃² = 50² + 53.33²

= 2500 + 2844.09

= 5344.09

L₃ = √5344.09

= 73. 10 yds

To distance covered = L₁ + L₂ + L₃

= 56.96 + 61.19 + 73.10

= 191.25 yards.