Question Number 183628 by a.lgnaoui last updated on 27/Dec/22
$${surface}\:{du}\:{rectangle}? \\ $$
Commented by a.lgnaoui last updated on 27/Dec/22
Commented by Frix last updated on 27/Dec/22
$${a}+\mathrm{9}={b}+\mathrm{2}={r} \\ $$$$\Rightarrow \\ $$$${b}={a}+\mathrm{7}\wedge{r}={a}+\mathrm{9} \\ $$$$ \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +\left({a}+\mathrm{7}\right)^{\mathrm{2}} =\left({a}+\mathrm{9}\right)^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} −\mathrm{4}{a}−\mathrm{32}=\mathrm{0} \\ $$$$\left({a}−\mathrm{8}\right)\left({a}+\mathrm{4}\right)=\mathrm{0} \\ $$$$\Rightarrow \\ $$$${a}=\mathrm{8}\wedge{b}=\mathrm{15}\wedge{r}=\mathrm{17} \\ $$$$\mathrm{Area}\:=\:\mathrm{120} \\ $$
Answered by HeferH last updated on 27/Dec/22
$$\left({R}\:−\:\mathrm{9}\right)^{\mathrm{2}} \:+\:\left({R}\:−\:\mathrm{2}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$$\:{R}^{\mathrm{2}} \:+\:\mathrm{81}\:−\:\mathrm{18}{R}\:+\:{R}^{\mathrm{2}} \:+\mathrm{4}\:−\:\mathrm{4}{R}\:=\:{R}^{\mathrm{2}} \\ $$$$\:{R}^{\mathrm{2}} \:−\:\mathrm{22}{R}\:+\:\mathrm{85}\:\:=\:\:\mathrm{0}\: \\ $$$$\:\left({R}\:−\:\mathrm{5}\right)\left({R}\:−\:\mathrm{17}\right)\:=\:\mathrm{0}\: \\ $$$$\:{R}\:=\:\mathrm{9}\:+\:…\:\Rightarrow\:{R}\neq\mathrm{5}\: \\ $$$$\:{R}\:=\:\mathrm{17} \\ $$$$\:{Area}\:=\:\left(\mathrm{17}−\mathrm{9}\right)\left(\mathrm{17}−\mathrm{2}\right)=\mathrm{8}\centerdot\:\mathrm{15}\:=\:\mathrm{120} \\ $$