Respostas

  • Usuário do Brainly
2014-06-24T15:38:54-03:00
H (hipotenusa) = 2x + 4
c₁ (cateto) = 2x + 2
c₂ (cateto) = 2x

h² = c₁² + c₂²
(2x + 4)² = (2x + 2)² + (2x)²
(2x + 4) . (2x + 4) = (2x + 2) . (2x + 2) + (2x) . (2x)
4x² + 8x + 8x + 16 = 4x² + 4x + 4x + 4 + 4x²
4x² - 4x² - 4x² + 8x + 8x - 4x - 4x + 16 - 4 = 0
- 4x² + 8x + 12 = 0
a = - 4, b = 8, c = 12
Δ = b² - 4 . a . c
Δ = 8² - 4 . (- 4) . 12
Δ = 64 + 192
Δ = 256

x = (- b ± √Δ)/(2 . a)
x = (- 8 ± √256)/(2 . (- 4))
x = (- 8 ± 16)/- 8

x' = (- 8 + 16)/- 8
x' = 8/- 8
x' = - 8/8
x' = - 1

x'' = (- 8 - 16)/- 8
x'' = - 24/- 8
x'' = 24/8
x'' = 3

S = {- 1, 3}

HIPOTENUSA = h

2x + 4
2 . 3 + 4
6 + 4
10

CATETO = c


2x + 2
2 . 3 + 2
6 + 2
8

CATETO = c


2x
2 . 3
6