Question Number 198054 by necx122 last updated on 09/Oct/23
$${In}\:\bigtriangleup{MNO},\:{MN}=\mathrm{6}{units},\:{MO}=\mathrm{4}\:{units} \\ $$$${and}\:{NO}=\mathrm{12}\:{units}.\:{If}\:{the}\:{bisector}\:{of}\:{the} \\ $$$${angle}\:{M}\:{meets}\:{NO}\:{at}\:{P},\:{calculate}\:{NP}. \\ $$
Commented by som(math1967) last updated on 09/Oct/23
$${But}\:{MN}+{MO}=\mathrm{10} \\ $$$${NO}=\mathrm{12} \\ $$$${MN}+{MO}<{NO} \\ $$$${Triangle}\:{possible}? \\ $$
Commented by necx122 last updated on 09/Oct/23
$${The}\:{amswer}\:{you}\:{gave}\:{initially}\:{was}\:{the} \\ $$$${same}\:{that}\:{the}\:{textbook}\:{gave}\:{but}\:{I}\:{didnt} \\ $$$${understand}\:{it}.\:{Please}\:{can}\:{you}\:{or}\:{anyone} \\ $$$${solve}\:{with}\:{a}\:{clear}\:{explanation}.\:{Thanks} \\ $$$${in}\:{advamce}. \\ $$
Commented by som(math1967) last updated on 10/Oct/23
$${In}\:\bigtriangleup{MNO}\:,\:{bisector}\:{of}\:\angle{M} \\ $$$${cut}\:{NO}\:{at}\:{P} \\ $$$${then}\:\frac{{MN}}{{MO}}=\frac{{NP}}{{PO}} \\ $$$${let}\:{MN}={m},\:\:{MO}={n} \\ $$$$\therefore\:\frac{{NP}}{{PO}}=\frac{{m}}{{n}}\Rightarrow{NP}\::\:{PO}={m}\::\:{n} \\ $$$${if}\:{NO}={x}\:{units} \\ $$$${then}\:{NP}={x}×\frac{{m}}{\left({m}+{n}\right)}\:{units} \\ $$$${PO}={x}×\frac{{n}}{\left({m}+{n}\right)}\:{units} \\ $$