A rectangular solid has length $5$ cm, width $4$ cm and diagonal $5\sqrt{2}$ cm. Its height is —

The space diagonal satisfies $d^2 = l^2 + w^2 + h^2$. So $(5\sqrt{2})^2 = 5^2 + 4^2 + h^2 \Rightarrow 50 = 41 + h^2 \Rightarrow h^2 = 9$, giving height $3$ cm.