Mathematics - Differentiation Question with Solution | TestHub

Diagonal $\mathrm{D}=\sqrt{2}$ a Differentiating w.r.t. t: $\frac{\mathrm{dD}}{\mathrm{dt}}=\sqrt{2}\frac{\mathrm{da}}{\text{ at }}$ or $\frac{\mathrm{da}}{\mathrm{dt}}=\frac{1}{\sqrt{2}}\frac{\mathrm{da}}{\mathrm{dt}}=\frac{1}{\sqrt{2}}\times 0.5\mathrm{cm}/\mathrm{s}$ Let Area is denoted by $\underline{A}$ $\frac{\mathrm{dA}}{\mathrm{dt}}=2\mathrm{a}\frac{\mathrm{da}}{\mathrm{dt}}$ when area $A$ is $400{\mathrm{cm}}^2$ then $\mathrm{a}=20$ $\therefore \frac{\mathrm{dA}}{\mathrm{dt}}=2\times 20\times \frac{0.5}{\sqrt{2}}=10\sqrt{2}{\mathrm{cm}}^2/\sec$