Question

A circle has a diameter of 9cm and a square has a side length of 5 cm.

Use pythagoras theorem to show that the square will fit inside the circle without touching the edges of the circle

Answer 1

Yes, the square will fit inside the circle without touching the edges.

Explanation:

To show that the square will fit inside the circle without touching the edges, we have to prove the length of the diagonal is less than the diameter of the circle.

Let's find the diagonal of the square using Pythagorean theorem.

diagonal² = side² + side²

= 5² + 5²

= 25 + 25

= 50

`\sf diagonal = √(50)`

`\sf = √(5*5*2)\\\\=5√(2)\\\\=5* 1.4142\\\\= 7.0710\\\\=7.07 \ cm`

7.07 < 9

Diagonal of square is less than the diameter of the circle.

So, the square will fit inside the circle without touching the edges.