Solution
= Solution
Differentiate before substituting the instantaneous side length. The <related rates> equation is
$$
2d\dot d=2b\dot b,\qquad \dot d=\frac b{\sqrt{a^2+b^2}}\dot b.
$$
At the stated dimensions and rate,
$$
\boxed{\dot d=\frac{30}{\sqrt{10^2+30^2}}\,4
=\frac{12}{\sqrt{10}}\ \mathrm{cm\,s^{-1}}
\approx3.795\ \mathrm{cm\,s^{-1}}.}
$$
The diagonal grows more slowly than the changing side, since $b/d<1$.