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Question Number 180258 by mr W last updated on 09/Nov/22

Commented by mr W last updated on 09/Nov/22

$$findtheareaofsquare.$$

Answered by HeferH last updated on 09/Nov/22

$$\frac{AF}{DE}=\frac{FB}{AD}\Rightarrow \frac{\sqrt{x^2-9}}{2}=\frac{3}{x}$$$$x^2(x^2-9)=36$$$$x^4-9x^2-36=0$$$$\left(thereisprobablyabettermethod\right)$$$$$$$$$$

Commented by mr W last updated on 10/Nov/22

$$thanks!$$

Answered by Acem last updated on 09/Nov/22

$$\mathrm{\angle }FAB=\mathrm{\angle }DEA=\alpha$$$$\sin \alpha =\frac{3}{x}=\frac{x}{\sqrt{x^2+4}}\Rightarrow x^4-9x^2-36=0$$$$\Rightarrow (x^2-12)(x^2+3)=0$$$$\Rightarrow x=2\sqrt{3}$$$$\Rightarrow Surface=12{un}^2$$$$p.s.\alpha =\frac{\pi }{3}$$

Commented by mr W last updated on 10/Nov/22

$$thanks!$$

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