Question

Find the side of a square whose diagonal is \( 10\sqrt{2} \, \text{cm} \):

Hint:

The diagonal of a square is always \( \sqrt{2} \) times the length of its side.

Answer 1

Step 1: The diagonal \( d \) of a square relates to its side \( a \) by: \[ d = a\sqrt{2}. \] Step 2: Substituting \( d = 10\sqrt{2} \, \text{cm} \): \[ 10\sqrt{2} = a\sqrt{2}. \] Step 3: Dividing both sides by \( \sqrt{2} \): \[ a = 10 \, \text{cm}. \]