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 182694 by cherokeesay last updated on 13/Dec/22

Answered by HeferH last updated on 13/Dec/22

Commented by HeferH last updated on 13/Dec/22

$$r\sqrt{3}+r=3$$$$r=\frac{3}{\sqrt{3}+1}$$$${OO}^{\prime 2}={(2\sqrt{3}-r)}^2+{\left(r\sqrt{3}\right)}^2$$$$=12+r^2-4r\sqrt{3}+3r^2$$$$=12+4r^2-4r\sqrt{3}$$$$=\sqrt{4(3+r^2-r\sqrt{3}})=2\sqrt{3+r^2-r\sqrt{3}}$$$$=2\sqrt{3+{\left(\frac{3\sqrt{3}-3}{2}\right)}^2-\frac{(3\sqrt{3}-3)\sqrt{3}}{2}}$$$$=\sqrt{4\left(\frac{15-6\sqrt{3}}{2}\right)}=\sqrt{30-12\sqrt{3}}$$$$$$$$=\cancel{\sqrt{22-8\sqrt{3}}}$$

Commented by cherokeesay last updated on 13/Dec/22

$$$$$$\mathrm{there}\mathrm{error}\mathrm{in}\mathrm{your}\mathrm{calculations}\mathrm{we}\mathrm{mustv}$$$$\mathrm{hae}\mathrm{as}\mathrm{a}\mathrm{result}:\sqrt{30-12\sqrt{3}}\backsimeq 3.056...$$

Commented by HeferH last updated on 13/Dec/22

$$Thatstrue,Ivecorrectit:)$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com