 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $b_0=b(0)$ in centimetres and take $t$ in seconds. The constant rate gives $b(t)=b_0+4t$. By the <Pythagorean theorem>, the diagonal length is
$$
\boxed{d(t)=\sqrt{100+(b_0+4t)^2}\ \mathrm{cm},}
$$
for times when the side length is nonnegative. No initial value of $b$ is specified, so it must remain as a parameter. Choosing the time origin when $b=0$ gives the special convention $d(t)=\sqrt{100+16t^2}\,\mathrm{cm}$.

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