Question Number 166319 by cortano1 last updated on 18/Feb/22
Commented by otchereabdullai@gmail.com last updated on 18/Feb/22
$$\mathrm{nice}\:\mathrm{question} \\ $$
Commented by MJS_new last updated on 18/Feb/22
$$\mathrm{for}\:\mathrm{any}\:\mathrm{given}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\mathrm{and} \\ $$$${a}\:\mathrm{being}\:\mathrm{the}\:\mathrm{base}\:\mathrm{line}\:\left(\mathrm{orientation}\:\mathrm{as}\:\mathrm{in}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{given}\:\mathrm{picture}\right): \\ $$$$\mid{DE}\mid=\frac{\delta{a}}{\delta+{a}^{\mathrm{2}} }\:\mathrm{with}\:\delta=\sqrt{\left({a}+{b}+{c}\right)\left({b}+{c}−{a}\right)\left({a}+{c}−{b}\right)\left({a}+{b}−{c}\right)} \\ $$
Answered by mr W last updated on 18/Feb/22
$$\mathrm{5}{h}=\mathrm{3}×\mathrm{4}\:\Rightarrow{h}=\mathrm{2}.\mathrm{4} \\ $$$$\frac{\mathrm{2}{r}}{\mathrm{5}}=\frac{\mathrm{2}.\mathrm{4}−{r}}{\mathrm{2}.\mathrm{4}} \\ $$$${r}=\frac{\mathrm{60}}{\mathrm{49}} \\ $$$${DE}=\mathrm{2}{r}=\frac{\mathrm{120}}{\mathrm{49}}\approx\mathrm{2}.\mathrm{449} \\ $$
Commented by Tawa11 last updated on 18/Feb/22
$$\mathrm{Great}\:\mathrm{sir} \\ $$