Question

A walkway forms one diagonal of a square playground. The walkway is 28 m long. How long is a side of the playground?

Answer 1

Length of side of playground is 19.798 meter

Solution:

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,

$PR^2 = PQ^2 + RQ^2$

$28^2 = a^2 + a^2\\\\2a^2 = 784\\\\a^2 = 392\\\\a =19.798$

Thus the length of side of playground is 19.798 meter