Question

Triunghiul MNP - dreptunghic in M. CtgN=2 cm, MP=5 cm. Calculati perimetrul si aria triunghiului
MNP.

Answer 1

       
ctg <N = 2
=> MN / MP = 2     dar MP = 5 cm
=> MN = 2 * 5 = 10 cm
NP o calculam cu Pitagora.

$NP = \sqrt{MN^2 + MP^2}=\sqrt{10^2 + 5^2}=\sqrt{100 + 25}= \sqrt{125}=5 \sqrt{5} \;cm$

$P=MN+MP+NP=10+5+5 \sqrt{5}= \\ =15+5 \sqrt{5}\;cm=\boxed{5(3+\sqrt{5})cm} \\ \\ A = \frac{MN*MP}{2}= \frac{10*5}{2} = 5*5=\boxed{25 \;cm^2}$