Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 160924 by amin96 last updated on 09/Dec/21

Commented by amin96 last updated on 09/Dec/21

$$$$green area=? H orthogonal center

Answered by mr W last updated on 09/Dec/21

Commented by mr W last updated on 09/Dec/21

$$\frac{y}{7}=\frac{x}{2}$$$$\Rightarrow y=\frac{7x}{2}$$$$\frac{x+7}{b}=\frac{y+2}{6}=\frac{\frac{7x}{2}+2}{6}=\frac{7x+4}{12}$$$$\Rightarrow b=\frac{12(x+7)}{7x+4}$$$$AF\times 7=by=\frac{12(x+7)}{7x+4}\times \frac{7x}{2}$$$$\Rightarrow AF=\frac{6x(x+7)}{7x+4}$$$$BF=\sqrt{2^2-x^2}=\sqrt{4-x^2}$$$$\frac{6x(x+7)}{7x+4}+\sqrt{4-x^2}=6$$$$\sqrt{4-x^2}=\frac{6(4-x^2)}{7x+4}$$$$6\sqrt{4-x^2}=7x+4$$$$36(4-x^2)=49x^2+16+56x$$$$85x^2+56x-128=0$$$$x=\frac{-28+108}{85}=\frac{16}{17}$$$$b=\frac{12(\frac{16}{17}+7)}{7\times \frac{16}{17}+4}=9$$$$A_{green}=\frac{1}{2}\times 2\times 9=9$$

Commented by Tawa11 last updated on 09/Dec/21

$$\mathrm{Great}\mathrm{sir}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com