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Question Number 189233 by a.lgnaoui last updated on 13/Mar/23

$$1\bullet Evaluer:\mathit{A}\mathit{i}\mathit{r}\mathit{e}\left({\mathit{A}}^{\prime }{\mathit{B}}^{\prime }{\mathit{C}}^{\prime }{\mathit{D}}^{\prime }\right)$$$$2\bullet Endeduire:\frac{\mathit{A}\mathit{i}\mathit{r}\mathit{e}\left({\mathit{A}}^{\prime }{\mathit{B}}^{\prime }{\mathit{C}}^{\prime }{\mathit{D}}^{\prime }\right)}{\mathit{A}\mathit{i}\mathit{r}\mathit{e}\left(\mathit{A}\mathit{B}\mathit{C}\mathit{D}\right)}$$

Commented by a.lgnaoui last updated on 13/Mar/23

$$\left[\mathit{A}{}^{\prime }{\mathit{B}}^{\prime }\mathit{D}\right]alignes$$

Commented by a.lgnaoui last updated on 13/Mar/23

Answered by HeferH last updated on 14/Mar/23

Commented by HeferH last updated on 14/Mar/23

$$\{\begin{array}{l}3\mathrm{a}=\frac{\mathrm{b}}{\sqrt{3}}\\ \mathrm{a}\sqrt{3}+\mathrm{b}=5\sqrt{3}\end{array}$$$$\bullet 3\mathrm{a}\sqrt{3}+\mathrm{a}\sqrt{3}=5\sqrt{3}$$$$\mathrm{a}=\frac{5}{4}\Rightarrow \mathrm{b}=\frac{15\sqrt{3}}{4}$$$$\bullet \mathrm{a}\times \mathrm{b}=\frac{75\sqrt{3}}{16}$$$$\bullet \frac{\mathrm{Area}\left({\mathrm{A}}^{\prime }{\mathrm{B}}^{\prime }{\mathrm{C}}^{\prime }{\mathrm{D}}^{\prime }\right)}{\mathrm{Area}\left(\mathrm{ABCD}\right)}=\frac{75\sqrt{3}}{16}\times \frac{1}{25\sqrt{3}}=\frac{3}{16}$$

Commented by a.lgnaoui last updated on 14/Mar/23

$$exactly.thankyou$$

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