Question

In triunghiul DEF dreptunghic in E si EA_|_DF,se dau DF=10 cm si AD=3AE.
Aflati AD,AF si AE

Answer 1

Din teorema inaltimii obtinem:

$AE^{2}=AD*AF <=> AE^{2}=3*AE*AF<=>AE=3*AF$

AD=3*AE=3*3*AF=9*AF

AD+AF=DF=10 <=> 9AF+AF=10 <=> 10AF=10 => AF=1 (cm) => AD=9*1=9(cm).

AD=3*AE=> AE=$\frac{AD}{3}= \frac{9}{3}=3(cm).$