Length of side of playground is 19.798 meter
Given that a walkway forms one diagonal of a square playground
The walkway is 28 m long
To find: To find length of side of playground
The diagram is attached below
Consider the figure PQRS is a sqaure
Let us assume the length of side of the square is "a"
PQ forms the diagonal which is 28 m long
PQR forms a right angled triangle with PR as hypotenuse
And PQ and RQ forms the other two legs of right angled triangle
By pythogoras theorem,
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
By above definition we get,
[tex]PR^2 = PQ^2 + RQ^2[/tex]
[tex]28^2 = a^2 + a^2\\\\2a^2 = 784\\\\a^2 = 392\\\\a =19.798[/tex]
Thus the length of side of playground is 19.798 meter
