Question

1. In triunghiul MNP, masura unghiului M = 90 de grade, avem [MN]=[MP].
a) Daca NP = 24 cm, calculati MN.
b) Daca NP = 8$\sqrt{2}$ cm ,calculati MP.
c) Daca MN = 12 cm , calculati NP.
d) Daca Mp = 18[tex] \sqrt{2}
[/tex] cm , calculati NP.

4. In triunghiul dreptunghic ABC, masura unghiului A = 90 de grade, AD _|_ BC, D ∈ (BC), se cunosc lungimile a doua segmente :
a) AC= 20cm si AB= 15 cm. Calculati AD,BD,BC,DC.
b) BC= 40cm si AB=24 cm. Calculati AC,BD,DC,AD.

Answer 1

1. In triunghiul MNP, masura unghiului M = 90 de grade, avem [MN]=[MP].
a) Daca NP = 24 cm, calculati MN.
MN=MP=x
NP²=x²+x²=2x²
24²=2x²
x=√576/2=√288=12√2
b) Daca NP = 8 cm ,calculati MP.
MN=MP=x
NP²=x²+x²=2x²
(8√2)²=2x²
128=2x²
x=√128/2=√64=8
c) Daca MN = 12 cm , calculati NP.
MN=MP=12
NP²=12²+12²=288
NP=√288=12√2
d) Daca MP = 18 cm , calculati NP.
MN=MP=18√2
NP²=(18√2)²+(18√2)²=648+648=1296
NP=√1296=36

4. In triunghiul dreptunghic ABC, masura unghiului A = 90 de grade, AD _|_ BC, D ∈ (BC), se cunosc lungimile a doua segmente :
a) AC= 20cm si AB= 15 cm. Calculati AD,BD,BC,DC.
BC=√(20²+15²)=√(400+225)=√625=25
AB²=BDxBC
15²=BDx25
BD=225/25=9
DC=25-9=16
AD=√9x16=√144=12
b) BC= 40cm si AB=24 cm. Calculati AC,BD,DC,AD.
AC=√(40²-24²)=√(1600-576)=√1024=32
AB²=BDxBC
576=BDx40
BD=574/40=14,4
DC=40-14,4=25,6 
AD=√14,4x25,6=√368,64=19,2