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Question Number 218528 by Spillover last updated on 11/Apr/25

Answered by mr W last updated on 11/Apr/25

Commented by mr W last updated on 11/Apr/25

$$3\theta =\frac{\pi }{2}\Rightarrow \theta =\frac{\pi }{6}=30°$$$$a\sin \theta +4\cos \theta =4$$$$\Rightarrow a=8(1-\frac{\sqrt{3}}{2})$$$$lengthofbigrectangleb:$$$$b=a+a\cos \theta +2a\sin \theta +\frac{a}{\tan \theta }+4$$$$b=8(1-\frac{\sqrt{3}}{2})(1+\frac{\sqrt{3}}{2}+2\times \frac{1}{2}+\sqrt{3})+4=2+4\sqrt{3}$$$$areaofbigrectangle:$$$$4\times b=8(1+2\sqrt{3})✓$$$$areaofsmallrectangle:$$$$4\times a=16(2-\sqrt{3})✓$$

Answered by Spillover last updated on 11/Apr/25

Answered by Spillover last updated on 11/Apr/25

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