Question

In figura 5, abc reprezinta un teren agricol. Pe teren se planteaza meri, pe randurile m1n1, m2n2, m3n3 si m4n4. Daca an1=3m, bc=12m, am1=m1m2=m2m3=m3m4=m3b=2m, iar m1n1 paralel cu m2n2 paralel cu m3n3 paralel cu m4n4 paralel cu bc, calculati lungimea gardului ce inconjoara terenul abc​.

Answer 1

Ipoteza:

AN₁=3 m

BC=12 m

AM₁=M₁M₂=M₂M₃=M₃M₄=M₄B=2 m

Rezolvare:

AB=AM₁+M₁M₂+M₂M₃+M₃M₄+M₄B

AB=5AM₁=10 m

M₁N₁ ║ M₂N₂⇒T.Thales

$\frac{AM_1}{AM_2} =\frac{AN_1}{AN_2} \\\\\frac{2}{4}=\frac{3}{AN_2}$

AN₂=6 m

M₁N₁ ║ BC⇒  T.Thales

$\frac{AM_1}{AB} =\frac{AN_1}{AC} \\\\\frac{2}{10} =\frac{3}{AC}$

AC=15 m

P=AB+AC+BC=10+15+12=37 m