Question

Fie triunghiul ABC cu m(unghiului A)=90 de grade si AD perpendicular pe BC,D apartine lui BC.
Daca BD/DC=2/7 si BC=18 cm,calculati BD,DC,AB si AC.

Answer 1

[tex] \frac{BD}{DC} = \frac{2}{7} =\ \textgreater \ BD= \frac{2*DC}{7} \\ BC=BD+DC=\ \textgreater \ 18= \frac{2*DC}{7} +DC \\ 18= \frac{9DC}{7 } \\ DC=14 \\ BD=4 \\ TEOREMA-CATETEI:AB ^{2} =BD*BC \\ AB ^{2} =4*18 \\ AB ^{2} =72 \\ AB=6 \sqrt{2} \\TEOREMA -LUI-PITAGORA: BC ^{2} =AB ^{2} +AC ^{2} \\ AC ^{2} =BC ^{2} -AB ^{2} \\ AC ^{2} =324-72 \\ AC ^{2} =252 \\ AC=6 \sqrt{7} [/tex]