Question

Teorema de Pitágoras
Encontre os valores desconhecidos das figuras abaixo:

Answer 1

a) n^2 = 3^2 + 4^2 => n^2 = 25 => n = 5
(V29)^2 = x^2 + 5^2
x^2 = 29 - 25
x^2 = 4
x = 2

b) n^2 = 2^2 + 2^2 => n^2 = 8 => n = 2V2
x^2 = (2V2)^2 + 2^2 => x^2 = 8 + 4 => x^2 = 12 => x = 2V3

c) (3V11)^2 = x^2 + (2V3)^2
x^2 = 99 - 12 => x^2 = 87 => x = V87

d) (x + 1)^2 = x^2 + 3^2
x^2 + 2x + 1 = x^2 + 9
2x + 1 = 9
2x = 8
x = 8/2 = 4

e) (2V13)^2 = x^2 + (x + 2)^2
52 = x^2 + x^2 + 4x + 4
2x^2 + 4x - 48 = 0
x^2 + 2x - 24 = 0
delta = 4 + 96 = 100 => Vdelta = 10
x = (-2 +/- 10)/2
x’ = (-2 - 10)/2 = -12/2 = -6 ❌
x’’ = (-2 + 10)/2 = 8/2 = 4 ✅

2)
13^2 = x^2 + 5^2
x^2 = 169 - 25
x^2 = 144
x = 12

5^2 = y^2 + 4^2
y^2 = 25 - 16
y^2 = 9
y = 3

Distância AB = x + y = 12 + 3 = 15.