Question

In the diagram shown , the length of a side of the square is x cm , where x∈ℝ. Find the length of the diagonal of the square in terms of x

Answer 1

Consider the figure below

The diagonal of the square is shown

Using Pythagoras theorem, it follows:

`d^2=x^2+x^2`

Solve the equation for d

`\begin{gathered} d^2=2x^2 \\ d=\sqrt[]{2x^2} \\ d=x\sqrt[]{2} \end{gathered}`

Therefore the diagonal of the square is

`d=x\sqrt[]{2}`