Question

Aflati lungimile laturilor AB si BC ale paralelogramului ABCD, stiind ca AB si BC sunt direct proportionale cu 4 si 6 iar perimetrul paralelorgramului este egal cu 1,8m

Answer 1

$ABCD-paralelogram \\ AB=CD \\ BC=AD \\\\\\ AB;BC \ \ \ d.p \\ 4;6 \\\\\\ \frac{AB}{4}=\frac{BC}{6}=k \\\\ AB=4k \\ BC=6k \\\\ P=1,8 \\\\ P=2*AB+2*BC \\\\ P=2(4k+6k) \\\\ P=2*10k \\\\ 2*10k=1,8 \\\\ k=\frac{1,8}{20} \\\\ \underline{k=0,09} \\\\\\ AB=4*0,09 \\\\ \boxed{AB=0,36} \\\\ BC=6*0,09 \\\\ \boxed{BC=0,54}$

Answer 2

{AB;BC} d.p. {4;6}=>AB/4=BC/6=K=>AB=4K si BC=6K; AB+BC+CD+AD=1,8 m; 2AB+2BC=180 cm; AB+BC=90 cm; 4K+6K=90 cm; 10K=90=>K=9 cm=>AB=36 cm si CD=54 cm