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Question Number 194463 by Mingma last updated on 08/Jul/23

Answered by mr W last updated on 08/Jul/23

Commented by Mingma last updated on 08/Jul/23

How did you calculate 1%?

Commented by mr W last updated on 08/Jul/23

$$d=2c$$$$R=\frac{a+b+2c+2d}{2}=\frac{a+b}{2}+3c$$$$a^2=2c(a+b+2d)=2c(a+b)+8c^2$$$$b^2=2d(a+b+2c)=4c(a+b)+8c^2$$$$b^2-a^2=2c(a+b)$$$$\Rightarrow c=\frac{b-a}{2}$$$$a^2=(b-a)(a+b)+2{(b-a)}^2$$$$\Rightarrow 3b=4a$$$$\Rightarrow b=8c,a=6c$$$$\frac{c}{R}=\frac{c}{\frac{a+b}{2}+3c}=\frac{1}{7+3}=\frac{1}{10}$$$$\frac{areasmallcircle}{areabigcircle}=\frac{\pi c^2}{\pi R^2}={\left(\frac{c}{R}\right)}^2=\frac{1}{100}=1\mathrm{\%}$$

Commented by Mingma last updated on 09/Jul/23

Very detailed solution!

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