Δ ABC, m A=90
Construiesti inaltimea AD, obtii astfel proiectiile BD si DC
AB+AC=105
[tex] \frac{BD}{DC} =1 \frac{7}{9} = \frac{16}{9} =k[/tex]
DB=16k
DC=9k
AB²=BD*BC
AB²=16k*25k
AB²=400k²⇒AB=20k
AC²=DC*BC
AC²=9k*25k=225k²
AC=15k
AB+AC=105
20k+15k=105
35k=105
k=3
AB=20k=20*3=60 cm
AC=15k=15*3=45 cm
BC²=AB²+AC² ( aplici Pitagora in Δ BAC)
BC²=3600+2025=5625
BC=75 cm
A=[tex] \frac{AB*AC}{2} = \frac{60*45}{2} =1350 [/tex] cm²
P=60+45+75=180 cm
