LS=12 si QS=2*SP
Problema 1)
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
Problema 2)
In rombul ABCD, notam AC∩DB cu O.
AC=16⇒AO=OB=8
In ΔAOB dreptunghic in O, calculam cateta OB=√(AB²-AO²)=√(10²-8²)=6
In ΔAOB, dreptunghic in O, aplicam teorema catetei:
AO²=AM*AB⇒AM=AO²/AB=8²/10=6.4
OB²=MB*AB⇒MB=OB²/AB=6²/10=3.6
Aplicam teorema inaltimii: OM=√(AM*MB)=√(6.4*3.6)=4.8
In ΔCOD, dreptunghic in O, aplicam teorema catetei:
CO²=CN*DC⇒CN=8²/10=6.4
OD²=ND*DC⇒ND=6²/10=3.6
Aplicam teorema inaltimii: On=√(CN*ND)=√(6.4*3.6)=4.8
In final: MN=MO+ON =4.8+4.8=9.6
