Question

A square is drawn inside a circle so that its vertices touch the circle.if the radius of the circle is 15cm, what is the perimeter of the square?

Answer 1

Answer: 84.84cm

Explanation:

Since the vertices of the square touches the circle , it means that the diameter of the circle is the same as the diagonal of the square.

Diameter of a circle , given the radius = 2 x radius

Diameter of the circle is therefore 2 x 15 = 30cm

Recall that in a square the point where the diagonals intersect , divides each diagonal into two equal parts , and since the square touches the edge of the circle , it means that the length of the diagonal is 30.

We need to find the length of one side of the square , in order to find the perimeter . That means we will use Pythagoras rule, which states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

The hypotenuse is the unknown side ,let it be x and the other sides are 15 and 15

Therefore :

`x^(2)` =
`15^(2)` +
`15^(2)`

`x^(2)` = 225 + 225

`x^(2)` = 450

x =
`√(450)`

x ≈21.21

Therefore , the side of the square is 21.21

The formula for calculating the perimeter of a square is 4x,

Therefore : P = 4(21.21)

P = 84.84 cm