Question

in triunghiul ABC cu masura unghiului A=90 de grade, construim inaltimea AD,D apartine BC
a) daca AB=10 cm si BD=4cm, aflati CD

Answer 1

AD² = √AB² - BD² = √100 - 16 = √84 = 2√21 cm

AD² = BD×CD => CD = AD²/BD = 84/4 = 21 cm

Answer 2

Aplicăm teorema catetei :

$\it AB^2=BC\cdot BD \Rightarrow 10^2=BC\cdot 4 \Rightarrow 100=BC\cdot 4|_{:4} \Rightarrow BC=25\ cm\\ \\ \\ CD=BC-BD=25-4=21\ cm$