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 182910 by mnjuly1970 last updated on 16/Dec/22

Answered by mr W last updated on 16/Dec/22

a=side length of square  R=radius of circle  R^2 =(R−a)^2 +(R−(a/2))^2   5a^2 −12Ra+4R^2 =0  ⇒(a/R)=(2/5)  ⇒a=(2/5)×5=2 cm  area of square =a^2 =4 cm^2

$${a}={side}\:{length}\:{of}\:{square} \\ $$$${R}={radius}\:{of}\:{circle} \\ $$$${R}^{\mathrm{2}} =\left({R}−{a}\right)^{\mathrm{2}} +\left({R}−\frac{{a}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\mathrm{5}{a}^{\mathrm{2}} −\mathrm{12}{Ra}+\mathrm{4}{R}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\frac{{a}}{{R}}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\Rightarrow{a}=\frac{\mathrm{2}}{\mathrm{5}}×\mathrm{5}=\mathrm{2}\:{cm} \\ $$$${area}\:{of}\:{square}\:={a}^{\mathrm{2}} =\mathrm{4}\:{cm}^{\mathrm{2}} \\ $$

Commented by mnjuly1970 last updated on 16/Dec/22

grateful sir W

$${grateful}\:{sir}\:{W} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com