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Question Number 187589 by Mingma last updated on 19/Feb/23

Commented by Mingma last updated on 19/Feb/23

Blue area=?

Answered by cortano12 last updated on 19/Feb/23

$$\cos \alpha =\frac{{\left(5\sqrt{2}\right)}^2+{\left(5\sqrt{5}\right)}^2-5^2}{2.\left(5\sqrt{2}\right)\left(5\sqrt{5}\right)}$$$$\cos \alpha =\frac{50+125-25}{50\sqrt{10}}=\frac{3}{\sqrt{10}}$$$$\sin \alpha =\frac{1}{\sqrt{10}}$$$$\Rightarrow \cos \beta =\cos \beta ;\frac{x}{10}=\frac{10}{5\sqrt{5}}\Rightarrow x=4\sqrt{5}$$$$bluearea=\frac{1}{2}.5\sqrt{2}.4\sqrt{5}.\frac{1}{\sqrt{10}}=10$$$$$$

Commented by Mingma last updated on 19/Feb/23

Good!

Answered by mr W last updated on 19/Feb/23

$$blue=\frac{5}{2}\times (5-{\left(\frac{5}{5\sqrt{5}}\right)}^2\times 5)=10✓$$

Commented by Mingma last updated on 19/Feb/23

Good!

Answered by HeferH last updated on 19/Feb/23

Commented by HeferH last updated on 19/Feb/23

$$\frac{h}{5}=\frac{5}{5\sqrt{5}}$$$$h=\frac{5}{\sqrt{5}}=\sqrt{5};$$$${10}^2=5\sqrt{5}\cdot x$$$$x=\frac{100}{5\sqrt{5}}=\frac{20\sqrt{5}}{5}=4\sqrt{5}$$$$A=\frac{h\cdot x}{2}=\frac{4\sqrt{5}\cdot \sqrt{5}}{2}=10u^2$$

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