3. A square sheet of paper measures 55 centimeters on each side. What is the length of the diagonal of the paper? 18. __

## Step 1<br />The problem involves finding the length of the diagonal of a square. In a square, all sides are equal, and the diagonal divides the square into two congruent right-angled triangles. The Pythagorean theorem is applicable case, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.<br /><br />## Step 2<br />In this case, the sides of the square are the two legs of the right-angled triangle, and the diagonal is the hypotenuse. Therefore, the length of the diagonal can be calculated using the formula:<br />### \( \text{Diagonal} = \sqrt{\text{side}^2 + \text{side}^2} \)<br /><br />## Step 3<br />Substituting the given side length of 55 cm into the formula, we get:<br />### \( \text{Diagonal} = \sqrt{55^2 + 55^2} \)<br /><br />## Step 4<br />Calculating the above expression, we get the length of the diagonal as approximately 77.78 cm.