diagonal line question

Question

The coach of Esther's soccer team always gives the team a few options for the warm-up before practice. The option for today is to run from opposite corners of the soccer field (diagonally) 6 times or from end to end of the soccer field length-wise 7 times. 

dimension

125m x 85m. 

The first option is to run 6 diagonal runs. The second option is to run 7 field runs. Which option will give Esther the greatest distance?

Answer 1

To find the diagonal, consider the hypotenuse of the right triangle with the length of the field and the width of the field as legs. You can apply the Pythagorean Theorem - a^2 + b^2 = c^2.

125^2 + 85^2 = c^2, c^2 = 22850, c (the diagonal) is approximately 151.16. 6 diagonals is 151.16 * 6 = approximately 906.96.

The length of the field is 125, and 7 * 125 = 875.

Thus, the first option, running the diagonal 6 times, is the greater option.