Answer:
- x = 3
- Sides are 6, 8 and 10
Step-by-step explanation:
Use Pythagorean to find the value of x:
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
