Question

In triunghiul ABC,masura lui A=90,AD_|_BC,D apartine lui BC .Daca raportul ariilor triunghiului ADB si ADc=9 pe 16 si BC=25cm ,calculati AD

Answer 1

$\frac{ A_{ADB} }{ A_{ADC} }= \frac{9}{16}<=> \frac{AD*BD}{AD*DC}= \frac{9}{16}<=> \frac{BD}{DC}= \frac{9}{16}=>BD=9k~si~ \\ DC=16k .$

BD+DC=BC <=> 9k+16k=25 <=> 25k=25 => k=1 => BD=9 (cm) si DC=16 (cm).

Aplic teoream inaltimii in ΔABC-dreptunghic in A:

$AD= \sqrt{BD*DC}= \sqrt{9*16}=3*4=12(cm).$