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Question Number 177796 by mr W last updated on 09/Oct/22

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

$$findtheareaofthesquare.$$

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

$$\mathrm{\angle }DFE=90°$$$$sidelengthofsquareshouldbeunique.$$

Commented by Rasheed.Sindhi last updated on 09/Oct/22

$${You}^{\prime }reright\mathit{s}\mathit{i}\mathit{r}!$$

Commented by Rasheed.Sindhi last updated on 09/Oct/22

$$\mathit{S}\mathit{i}\mathit{r}Ithinkthattheareadepends$$$$uponBEorFC.Inotherwords$$$$theareaofsquareisnotunique.$$

Answered by mr W last updated on 09/Oct/22

$$BC=DC=s$$$$\mathrm{\Delta }EBF\sim \mathrm{\Delta }FCD$$$$\frac{BF}{3}=\frac{s}{4}\Rightarrow BF=\frac{3s}{4}$$$$FC=\sqrt{4^2-s^2}$$$$BF+FC=s$$$$\frac{3s}{4}+\sqrt{4^2-s^2}=s$$$$\Rightarrow s^2=\frac{16\times 16}{17}=\frac{256}{17}={square}^{\prime }sarea$$

Commented by Tawa11 last updated on 09/Oct/22

$$\mathrm{Great}\mathrm{sirs}$$

Answered by cortano1 last updated on 09/Oct/22

$$\mathrm{AD}=\mathrm{CD}=\mathrm{d}$$$$\mathrm{BF}=\mathrm{a},\mathrm{CF}=\mathrm{b}\Rightarrow \mathrm{d}=\mathrm{a}+\mathrm{b}$$$$\mathrm{AE}=\mathrm{c},\mathrm{BE}=\mathrm{f}\Rightarrow \mathrm{d}=\mathrm{c}+\mathrm{f}$$$$\{\begin{array}{l}{\mathrm{c}}^2+{\mathrm{d}}^2=25\\ {\mathrm{d}}^2+{\mathrm{b}}^2=16\\ {\mathrm{a}}^2+{\mathrm{f}}^2=9\end{array}$$$$\Rightarrow \mathrm{a}=\frac{3}{\sqrt{17}};\mathrm{b}=\frac{12}{\sqrt{17}}$$$$\Rightarrow \mathrm{c}=\frac{4}{\sqrt{17}};\mathrm{d}=\frac{16}{\sqrt{17}};\mathrm{f}=\frac{13}{\sqrt{17}}$$$$\mathrm{area}\mathrm{of}\mathrm{square}=\frac{256}{17}$$

Answered by cortano1 last updated on 09/Oct/22

$$\frac{256}{17}?$$

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

$$yes!$$

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