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Question Number 181496 by Acem last updated on 26/Nov/22

Answered by mr W last updated on 26/Nov/22

$$rectangleA=2xh$$$$x^2+{(x+h)}^2=R^2$$$$2x^2+2xh+h^2=R^2$$$$2x^2+A+\frac{A^2}{4x^2}=R^2$$$$\frac{dA}{dx}=0$$$$4x-\frac{2A^2}{4x^3}=0$$$$x^4=\frac{A^2}{8}\Rightarrow x^2=\frac{A}{2\sqrt{2}}$$$$2\times \frac{A}{2\sqrt{2}}+A+\frac{2\sqrt{2}{A}^2}{4A}=R^2$$$$(1+\sqrt{2})A=R^2$$$$\Rightarrow A=(\sqrt{2}-1)R^2=maximumarea$$

Commented by mr W last updated on 26/Nov/22

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