Question

In triunghiul ABC cu A= 90grade construim inaltimea AD, D apartine BC stiind ca:



a) AB=10cm si BD= 4cm calculati CD.

b) AC=12cm si CD=6cm calculati BD

Answer 1

Explicație pas cu pas:

A). Aplicăm teorema catetei

AB^=BDxBC

10^=4xBC

100 =4xBC

BC=100:4

BC=25 cm

CD=BC-BD

CD=25-4

CD=21 cm

B) AC^=CDxBC

12^=6xBC

144=6xBC

BC=144:6

BC=24cm

BD=BC-CD

BD=24-6

BD=18 cm

Answer 2

$\it a)\ \Delta DAB-dr,\ \widehat D=90^o,\ \stackrel{T.P.}{\Longrightarrow}\ AD^2=AB^2-BD^2=10^2-4^2= 84\\ \\ \\ \Delta ABC-dr,\ \widehat A=90^o,\ \stackrel{T.h.}{\Longrightarrow}\ AD^2=BD\cdot CD \Rightarrow 84=4\cdot CD|_{:4} \Rightarrow CD=21\ cm$