Question

1.Fie triunghiul dreptunghic LPQ cu m(QLP)=90,inaltimea LS de 12 si QS=2 ori SP. Calculati lungimile:LP,LQ,QP,SP SI SQ urgent

Answer 1

LS=12 si QS=2*SP
In ΔQLP, dreptunghic in L, aplicam teorema inaltimii: LS²=QS*SP ⇒12²=2*SP*SP⇒SP=√(12²/2)=√(144/2)=√72=8.5
QS=2*8.5=17
QP=QS+SP=17+8.5=25.5

Aplicam teorema catetei:
QL=√(QP*QS)=√(25.5*17)=20.82
LP=√(SP*QP)=√(8.5*25.5)=14.72