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Question-166888




Question Number 166888 by cherokeesay last updated on 01/Mar/22
Answered by mr W last updated on 01/Mar/22
Commented by mr W last updated on 01/Mar/22
A_1 =((3×4)/2)=6  r=((6×2)/(3+4+5))=1  A_2 =((4×4)/2)=8  R=((8×2)/(5+4+(√(17))))=((16)/(9+(√(17))))  ⇒(r/R)=((9+(√(17)))/(16))≈0.8202
$${A}_{\mathrm{1}} =\frac{\mathrm{3}×\mathrm{4}}{\mathrm{2}}=\mathrm{6} \\ $$$${r}=\frac{\mathrm{6}×\mathrm{2}}{\mathrm{3}+\mathrm{4}+\mathrm{5}}=\mathrm{1} \\ $$$${A}_{\mathrm{2}} =\frac{\mathrm{4}×\mathrm{4}}{\mathrm{2}}=\mathrm{8} \\ $$$${R}=\frac{\mathrm{8}×\mathrm{2}}{\mathrm{5}+\mathrm{4}+\sqrt{\mathrm{17}}}=\frac{\mathrm{16}}{\mathrm{9}+\sqrt{\mathrm{17}}} \\ $$$$\Rightarrow\frac{{r}}{{R}}=\frac{\mathrm{9}+\sqrt{\mathrm{17}}}{\mathrm{16}}\approx\mathrm{0}.\mathrm{8202} \\ $$
Commented by Tawa11 last updated on 01/Mar/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Commented by cherokeesay last updated on 02/Mar/22
very nice.  thank you so much.
$${very}\:{nice}. \\ $$$${thank}\:{you}\:{so}\:{much}. \\ $$

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