Question

Fie triunghiul ABC cu AB=AC, BB'_|_AC,BB'=4 cm , M apartine [BC], MN _|_ AC si MP _|_ AB.
Calculati MN+MP

Answer 1

Ai desenul atasat.

Exprimam aria ΔABC isoscel (cu AB=AC) in doua moduri:

Aria ΔABC=AriaΔAMC+AriaΔAMB

$\frac{BB'*AC}{2} = \frac{MN*AC}{2} + \frac{MP*AB}{2}$, adica (pentru ca AB=AC):

$\frac{BB'*AC}{2} = \frac{AC}{2} (MN+MP)$ si daca impartim prin $\frac{AC}{2}$ obtinem:

BB'=MN+MP=4 cm