Between which two consecutive whole numbers does the length of the diagonal fall?

Question

Which whole number is it closer to? Use the drop-down menus to show your answer. If one side is \sqrt{18}

Answer 1

To determine the length of the diagonal and between which two consecutive whole numbers it falls, we can apply the Pythagorean theorem.

Given that one side is \(\sqrt{18}\), we can assume the other side is also \(\sqrt{18}\) (in a right triangle scenario, since the question does not specify otherwise).

The formula to calculate the diagonal \(d\) (hypotenuse) when both sides are equal is:

\[ d = \sqrt{a^2 + b^2} \]

Substituting \(a = \sqrt{18}\) and \(b = \sqrt{18}\):

\[ d = \sqrt{(\sqrt{18})^2 + (\sqrt{18})^2} \] \[ d = \sqrt{18 + 18} \] \[ d = \sqrt{36} \] \[ d = 6 \]

Now we can analyze the solution. The diagonal \(d\) is exactly \(6\), which is a whole number itself.

Thus, it falls between the consecutive whole numbers \(5\) and \(6\) and is closer to \(6\).

Final Answers:

• The diagonal falls between: 5 and 6
• It is closer to: 6