Question Number 169105 by mr W last updated on 24/Apr/22
Commented by mr W last updated on 24/Apr/22
$${find}\:{MN}=? \\ $$
Answered by greougoury555 last updated on 24/Apr/22
$${MP}×\left(\mathrm{14}+{NQ}\right)=\mathrm{20}×\mathrm{12} \\ $$$$\left({MP}+\mathrm{14}\right)×{NQ}=\mathrm{24}×\mathrm{10} \\ $$$$\begin{cases}{\mathrm{14}{MP}+{MP}.{NQ}=\mathrm{240}}\\{\mathrm{14}{NQ}+{MP}.{NQ}=\mathrm{240}}\end{cases} \\ $$$$\Rightarrow{MP}={NQ} \\ $$$${let}\:{MP}={NQ}={a} \\ $$$$\Rightarrow{a}^{\mathrm{2}} +\mathrm{14}{a}−\mathrm{240}=\mathrm{0} \\ $$$$\Rightarrow\left({a}+\mathrm{24}\right)\left({a}−\mathrm{10}\right)=\mathrm{0};\:{a}=\mathrm{10}={MP}={NQ} \\ $$$$\Rightarrow{MN}\:=\:\mathrm{34} \\ $$
Commented by mr W last updated on 24/Apr/22
$${thanks}! \\ $$