Question

Answer 1

Xét ΔANC và ΔAMB có: 

\(\widehat{AMB}=\widehat{ANC}=90^o\)

\(\widehat{NAC}\) chung 

\(\Rightarrow\text{Δ}ANC\sim\text{ΔAMB}\left(g.g\right)\)

\(\Rightarrow\dfrac{AM}{AN}=\dfrac{AB}{AC}\)

\(\Rightarrow\dfrac{40}{40+MN}=\dfrac{60}{90+60}\)

\(\Rightarrow60\left(40+MN\right)=40\cdot150\)

\(\Rightarrow2400+60MN=6000\)

\(\Rightarrow60MN=3600\)

\(\Rightarrow MN=60\left(cm\right)\)

Vậy: ... 

Answer 2

Có \(MB // NC\) ( 2 bên bờ ao cá ), theo định lí Thales có :

`{AM}/{MN} = {AB}/{BC}`

\( \Leftrightarrow \frac{40}{MN}=\frac{60}{90}\\ \Leftrightarrow MN . 60 =40 . 90 \\ \Leftrightarrow MN . 60= 3600\\ \Leftrightarrow MN = 3600:60\\ \Leftrightarrow MN=60(m)\)

Vậy \(MN= 60(m)\)