As the mirror is an "square". So, the diagonal is the hypotenuse of the square. So:

20^2 = 2 * x^2.

x = sqrt(2) * 10

and the perimeter is 4 * x

4 * sqrt(2) * 10 = 40*1.4 ... near to 60.

If the diagonal is 20 inches the side will be \(\frac{20}{\sqrt{2\) since the diagonal is \((\text{ side of the square }) \times \sqrt{2}\) from the Pythagoras theorem. It is worth memorizing this formula.

Now, clearly the perimeter will be \( 4 \times side = 4 \times \frac{20}{\sqrt{2}} = \frac{80}{\sqrt{2}}\).

Now multiplying both the numerator and the denominator by \(\sqrt{2}\) we get \(\frac{80 \times \sqrt{2}}{2} = 40 \times \sqrt{2}\)

Now it is worth memorizing the values of square roots of numbers 1 to 10. The square root of \(2\) is approximately \(1.414\).

Thus \(40 \times \sqrt{2} = 40 \times 1.414\) which is approximately \(40 \times 1.5 = 60\)

The answer is Choice B.