Question

In triunghiul ABC cu m(<A)=90°,[AD] este inaltime.Completati tabelul alaturat.La punctul d) se considera BD>DC

Answer 1

a)AD^2=BD×DC=144 =>AD=12
BC=BD+DC =>BC=30

b)AB^2=BD×BC ; AB^2=6rad3×8rad3 =>AB^2=48×3=144 =>AB=12
AC^2=BC^2-AB^2 ; AC^2=192-144=48 =>AC=4rad3
AC^2=DC×BC ; 48=DC×8rad3 =>DC=48/8rad3=2rad3

c)AD^2=BD×DC ; 288=BD×18 =>BD=288/18=16
BC=BD+DC=16+18=34

d)AD^2=BD×DC =>BD×DC=144 =>BD=144/DC
BD+DC=25
144/DC + DC = 25 |×DC
DC^2 - 25DC + 144 = 0
delta=(-25)^2 - 4×144
delta=625-576=49 =>rad delta=7
DC1=(25-7)/2=9 =>BD=144:9=16
DC2=(25+7)/2=16 =>BD=144:16=9 Nu e bun pentru ca BD>DC