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

Answer:

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

Step-by-step 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

$d = \sqrt{30^2+30^2} = \sqrt{1800}\approx 42.42$.

Thus, the diagonal has (approximately) 42.42 yards.