Using area

The diagram below shows the square with area 72 cm$^2$ with the diagonal in red. Then 4 copies of the square are stuck together. Notice that the diagonals form another square, which is also shown on its own.

 

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The square formed by the diagonals occupies half of the area of the 4 blue squares, so it has the same area as 2 blue squares, which is 72 + 72 = 144 cm$^2$.

So a square with side length equal to the red diagonal has area 144 cm$^2$, which means the diagonal must be 12 cm, since 12 $\times$ 12 = 144.

Using Pythagoras' Theorem

The area of the square is $72$ cm$^2$, so theside length is $\sqrt{72}$. This is shown on the diagram below, which also shows the diagonal, marked $d$.

 

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Applying Pythagoras' Theorem gives $$\begin{align}\sqrt{72}^2+\sqrt{72}^2&=d^2\\

\Rightarrow 72+72&=d^2\\

\Rightarrow 144&=d^2\\

\Rightarrow 12&=d\end{align}$$ (since $d$ must be positive).