Question

In triunghiul ABC,dreptunghic in A,ducem inaltimea AD,D apartine BC.Daca AD=12cm si CD==6cm calculati lungimile segmentelor BD,AC si AB.​

Answer 1

Răspuns:

BD=24cm; AC=6radical(5);  AB=12radical(5)

Explicație pas cu pas:

Desenul, cred, il faci singur. Folosim teorema inaltimii:  AD^2=CD*BD, de unde  avem 12^2=6*BD, DE UNDE BD=144:6=24

aCUM FOLOSIM TEOREMA CATETEI:  AC^2=CD*CB, Deorece CD+DB=AB=6+24=30, obtinem:  AC^2=6*30, DE UNDE AC=radical(6*30)=radical(6*6*5)=6*radical(5)

Analog aflam cateta AB:   AB^2=BD*BC=24*30, de unde AB=radical(24*30)=radical(6*4*6*5)=6*2*radical(5)=12*radical(5)