Question

A field hockey field is a rectangle 60 yards by 100 yards. What is the length of the diagonal from one corner of the field to the opposite corner?

Short answer

The diagonal of the field is approximately 116.62 yards.

Step-by-step solution

Understanding the Problem

The field hockey rectangle measures 60 yards by 100 yards. Hence, to find the diagonal, one needs to see the field as a right triangle where the sides of the rectangle are the base and height and the diagonal is the hypotenuse.

Apply the Pythagorean theorem

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, let's substitute the known values into the formula: \( D^2 = 60^2 + 100^2 \)

Solve for the Diagonal D

To find the actual length of the diagonal, perform the calculations on the right side of the equation and then compute the square root of the result. Hence, \( D = \sqrt{3600 + 10000} = \sqrt{13600} \).

Computing the approximated Solution

Calculating the square root of 13600 gives an D approximately being 116.62 yards.