Mathematics - Application of Derivative Question with Solution | TestHub

Let base $=b$
Altitude (or perpendicular) $=\sqrt{h^2-b^2}$ Area, $\mathrm{A}=\frac{1}{2}\times$ base $\times$ altitude $=\frac{1}{2}\times b\times \sqrt{h^2-b^2}$ $\Rightarrow \frac{d\mathrm{A}}{db}=\frac{1}{2}\left[\sqrt{h^2-b^2}+b\cdot \frac{-2b}{2\sqrt{h^2-b^2}}\right]$ $=\frac{1}{2}\left[\frac{h^2-2b^2}{\sqrt{h^2-b^2}}\right]$ Put $\frac{d\mathrm{A}}{db}=0,\Rightarrow b=\frac{h}{\sqrt{2}}$ Maximumarea $=\frac{1}{2}\times \frac{h}{\sqrt{2}}\times \sqrt{h^2-\frac{h^2}{2}}=\frac{h^2}{4}$