Question

In triunghiul abc, masura unghiului abc =90°, BD perpendicular pe AC si AD supra DC = 4 supra 1. Daca AC =20 cm,aflati lungimile segmentelor AD, DC si BD                     Ajutor !

Answer 1

ΔABC, mas <B=90
BD _|_AC
BD-h

AD/DC=4

(AD+DC)/DC=4

AC/DC=4

20/DC=4

DC=20/4=5

AD=AC-DC
AD=20-5
AD=15

BD²= AD*DC
BD²= 15*5
BD= √75   =>BD=5√3

Answer 2

AC=20
AD/DC=4 => AD=4DC
AD=AC-DC
AC-DC=4DC
AC=5DC=20
DC=4
Din teorema catetei:

BC²=AD*AC=4*20
BC=2√20
AD=20-4=16
AB²=AD*AC=16*20
AB=4√20
BD²=CB²-CD²=80-16=64
BD=8