Question

Na figura, determine o valor do perímetro do ABC:

a) 75m
b) 125m
c) 150m
d) 200m
e) 225m

Answer 1

Resposta:

d) 200m

Explicação passo a passo:

Triângulo ADE:

DE = BC

cos30° = (BC)/50

√(3)/2 = (BC)/50

2(BC) = 50√3

BC = 50/2√3

BC = 25√3

sen30° = (AE)/50

1/2 = (AE)/50

2(AE) = 50(1)

2(AE) = 50

AE = 50/2

AE = 25

-------------------

Triângulo ABC:

BC = 25√3

EB = DC = 50

AE = 25

AB = AE + EB = 25 + 50 = 75

AC = √[(AB)² + (BC)²]

AC = √[75² + (25√3)²]

AC = √[5625 + 25²(√3)²]

AC = √[5625 + 625(3)]

AC = √[5625 + 1875]

AC = √7500

AC = √(2500(3))

AC = √2500√3

AC = √50²√3

AC = 50√3

P = AB + BC + AC

P = 75 + 25√3 + 50√3

P = 75 + 75√3

P ≈ 75 + 75(5/3)

P ≈ 75 + 25(5)

P ≈ 75 + 125

P ≈ 200m