Question

ABC
AD=h
D∈BC
BD=3
DC=12

Aflati: BC,AD,AB,AC

Answer 1

Răspuns:

Consider ABC tr.dr.

B

| D

|

A_______________C

BC=15 cm

t.h.=>AD^2=3•12=36 =>AD=6 cm

t.cat. =>AB^2=3•15=45 =>AB=3rad5 cm

t.cat. =>AC^2=12•15=180 =>AC=6rad5 cm

Answer 2

Răspuns:

AD=6

BD=3

DC=12

AB =6,70820393

AC=13,416407865

BC=15

Explicație pas cu pas:

BC=BD+CD  => BC=3+12 => BC=15

AD²=BD*DC

AD²=3*12

AD²=36      ; 36=6*6= 6²

AD²=6²    => AD=6 (inaltimea)

AB²=BC*BD

AB²=15*3

AB²=45       ; 45=9*5 = 3²*5

AB=3√5   => AB=6,70820393 ( catena 1)

AC²=BC*CD

AC²=15*12

AC²=180    ; 180=2²*3²*5=(2*3)²*5=6²*5

AC=6√5   => AC=13,416407865 (catena 2)