Question

A square playground has a perimeter of 120 yards. what is the length of a diagonal of the playground?

Answer 1

Perimeter of square, 4a = 120

a = 30

diagonal = a√2 = 30√2 yards OR 42.3 yards

Answer 2

The length of the diagonal of the playground is approximately 42.42 yards.

Explanation:

As the playground is square we know the formula for its perimeter:
`P=4l`, where
`l` stands for the length of the side of the playground. By the statement of the problem we know that
`P=4l=120 yd`, then it is not difficult to find that
`l=30` yards.

If we trace the diagonal we see that a right triangle is formed, where the diagonal is its hypotenuse, and its sides are the sides of the playground. Then, using Pythagoras theorem (we denote by
`d` the length of the diagonal), we have

`d = √(30^2+30^2) = √(1800)\approx 42.42`.

Thus, the diagonal has (approximately) 42.42 yards.