quantum mechanics - Heisenberg relation

Given that $A(k)=\frac{N}{k^2+\alpha^2}$, show that $\Delta k \Delta x >1$.

Considering the above example, according to my textbook, it is written that I must square the above function and determine when does the square fall to 1/3 of it's peak value. What does that mean, practically speaking?

This should enable me to determine a value for $\Delta k$. Similarly we proceed in order to determine $\Delta x$ but by squaring $\psi(x,0)$, the wave function and seeing where does it drop off to $1/3$ for it's peak value.