Question

1. Se considera triunghiul MNP ~ triunghiul ABC. Stiind ca :
a)AriaMNP supra AriaABC = 25/36, aflati MN/AB.
b)AriaMNP supra AriaABC = 16//49, aflati NP/BC.

2.Se considera triunghiul ABC ~ tringhiul DEF, stiind ca
a)AB = 7cm, BC = 8cm, CA = 10cm si PerimetruDEF = 75 cm, calculati DE, EF si FD;
b)DE = 7cm, EF = 9cm, FD = 12cm si PerimetruABC = 70 cm , calculati AB, BC si CA;

Answer 1

Răspuns:

Explicație pas cu pas:

1a)

Amnp/Aabc=25/36=k²   ⇒MN/AB=k=5/6

b)

Amnp/Aabc=16/49=k²  ⇒NP/BC=k=4/7

2

Pabc=7+8+10=25cm

Pdef=75cm           Pabc/Pdef=25/75=1/3=k

AB/DE=1/3        DE=3AB=3x7=21cm

BC/EF=1/3        EF=3BC=3x8=24cm

AC/FD=1/3       FD=3×CA=30cm

b)

Pdef=(7+9+12)=28cm

Pabc=70cm          

Pabc/Pdef=70/28=10/4=5/2=k

AB/DE=5/2     AB=5DE/2=5x7/2=35/2=17,5 cm

BC=EF×5/2     BC=9×5/2=45/2=22,5cm

CA=DF×5/2    CA=12×5/2=30cm