Question

In triunghiul ABC cu m(

Answer 1

$BD+CD=BC \Leftrightarrow BD+CD=5 \cdot BD \Leftrightarrow CD=4 \cdot BD. \\ \\ \underline{Teorema~inaltimii}:~AD^2=BD \cdot CD \Leftrightarrow 24^2=BD \cdot 4 BD \Leftrightarrow \\ \Leftrightarrow 24^2=4BD^2 \Rightarrow 2BD=24 \Rightarrow BD=12~(cm). \\ \\ BC=5 \cdot BD=5 \cdot 12=60 ~(cm). \\ \\ \boxed{BC=60~cm}$

Answer 2

AD e inaltime
BD=x si BC=5x
AB=√BD*BC=√5x²=x√5
AC=√DC*BC=√20x²=2√5x
AD=AB*AC/BC
24=x√5*2√5x/5x
24=10x²/5x
2x=24 deci x=12cm
BC=12*5=60cm