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Question-178299




Question Number 178299 by HeferH last updated on 14/Oct/22
Answered by mr W last updated on 15/Oct/22
Commented by mr W last updated on 15/Oct/22
sides of green triangles:  2a, 2b, 2R  we have (2a)^2 +(2b)^2 =(2R)^2   ⇒a^2 +b^2 =R^2   blue area =a^2 +b^2 =R^2 =10^2 =100
$${sides}\:{of}\:{green}\:{triangles}: \\ $$$$\mathrm{2}{a},\:\mathrm{2}{b},\:\mathrm{2}{R} \\ $$$${we}\:{have}\:\left(\mathrm{2}{a}\right)^{\mathrm{2}} +\left(\mathrm{2}{b}\right)^{\mathrm{2}} =\left(\mathrm{2}{R}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$${blue}\:{area}\:={a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={R}^{\mathrm{2}} =\mathrm{10}^{\mathrm{2}} =\mathrm{100} \\ $$
Commented by Tawa11 last updated on 15/Oct/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$

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