Question Number 206491 by cortano21 last updated on 16/Apr/24
Commented by cortano21 last updated on 16/Apr/24
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Answered by mr W last updated on 16/Apr/24
Commented by mr W last updated on 16/Apr/24
![8+a=(√2)(3+(√2)a) ⇒a=8−3(√2) [ABCD]=(((3+(√2)a)^2 −a^2 )/2)=(((3+(√2)a+a)(3+(√2)a−a))/2) =((55((√2)+1)((√2)−1))/2)=((55)/2)=27.5 cm^2](https://www.tinkutara.com/question/Q206498.png)
$$\mathrm{8}+{a}=\sqrt{\mathrm{2}}\left(\mathrm{3}+\sqrt{\mathrm{2}}{a}\right) \\ $$$$\Rightarrow{a}=\mathrm{8}−\mathrm{3}\sqrt{\mathrm{2}} \\ $$$$\left[{ABCD}\right]=\frac{\left(\mathrm{3}+\sqrt{\mathrm{2}}{a}\right)^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}}=\frac{\left(\mathrm{3}+\sqrt{\mathrm{2}}{a}+{a}\right)\left(\mathrm{3}+\sqrt{\mathrm{2}}{a}−{a}\right)}{\mathrm{2}} \\ $$$$=\frac{\mathrm{55}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{2}}=\frac{\mathrm{55}}{\mathrm{2}}=\mathrm{27}.\mathrm{5}\:{cm}^{\mathrm{2}} \\ $$
Answered by cortano21 last updated on 16/Apr/24
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