Calcola il perimetro dei seguenti triangoli :La retta nel piano cartesiano

A [-2, 1]

B [2, -2]

C [4, 4]

ΑΒ = √((2 + 2)^2 + (-2 - 1)^2) = 5

ΒC = √((4 - 2)^2 + (4 + 2)^2) = 2·√10

ΑC = √((4 + 2)^2 + (4 - 1)^2) = 3·√5

perimetro=5 + 2·√10 + 3·√5 = 18.03 circa

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50)

 Perimetro del triangolo ABC con i dati: $\small A(-2; 1); B(2; -2); C(4; 4):$

$\small 2p_{ABC}= \overline{AB}+\overline{BC}+\overline{AC}$

$\small2p_{ABC}=\sqrt{\left(A_x\small-B_x\right)^2+(A_y-B_y)^2}+\sqrt{(B_x-C_x)^2+(B_y-C_y)^2}+\sqrt{(A_x-C_x)^2+(A_y-C_y)^2}$

$\small 2p_{ABC}= \sqrt{(-2-2)^2+(1-(-2))^2}+\sqrt{(2-4)^2+(-2-4)^2}+\sqrt{(-2-4)^2+(1-4)^2}$

$\small 2p_{ABC}= \sqrt{(-4)^2+(1+2)^2}+\sqrt{(-2)^2+(-6)^2}+\sqrt{(-6)^2+(-3)^2}$

$\small 2p_{ABC}= \sqrt{16+3^2}+\sqrt{4+36}+\sqrt{36+9}$

$\small 2p_{ABC}= \sqrt{16+9}+\sqrt{40}+\sqrt{45}$

$\small 2p_{ABC}= \sqrt{25}+2\sqrt{10}+3\sqrt{5}$

$\small 2p_{ABC}= 5+2\sqrt{10}+3\sqrt{5}$ $\small \approx{18,033}.$

46

AB = 3

BC = 2√5 

AC = √17

perimetro 2p = 3+2√5+√17 = 11,60 cm 

47

AB = 2√10

BC = √13

AC = 5 

perimetro 2p = 2√10+5+√13 = 14,93

48

AB = 7

BC = √29

AC = 5√2

perimetro 2p = √29+5√2+7 = 19,46 

49

AB = √22,25

BC = √41

AC = √70,25

perimetro 2p = √22,25+√41+√70,25 = 19,50  

50

AB = 5

BC = 2√10

AC = 3√5

perimetro 2p = 5+2√10+3√5