Respuesta :

mhanifa

Answer:

  • x = 3
  • Sides are 6, 8 and 10

Step-by-step explanation:

Use Pythagorean to find the value of x:

  • c² = a² + b²

Consider:

  • a = x + 3, b = 3x - 1, c = 4x - 2

Substitute and solve for x:

  • (4x - 2)²  = (x + 3)² + (3x - 1)²
  • 16x² - 16x + 4 = x² + 6x + 9 + 9x² - 6x + 1
  • 16x² - 10x² - 16x + 4 - 10 = 0
  • 6x² - 16x - 6 = 0
  • 3x² - 8x - 3 = 0
  • 3x² - 9x + x - 3 = 0
  • 3x(x - 3) + (x - 3) = 0
  • (x - 3)(3x + 1) = 0
  • x - 3 = 0, 3x + 1 = 0
  • x = 3, x = - 1/3

Positive root is accepted only.

Sides of the triangle:

  • a = x + 3 = 3 + 3 = 6
  • b = 3x - 1 = 3*3 - 1 = 8
  • c = 4x - 2 = 4*3 - 2 = 10

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