Answer:
x = 4
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(3x + 1)² = (x + 1)² + (2x + 4)² ← expand all factors using FOIL
9x² + 6x + 1 = x² + 2x + 1 + 4x² + 16x + 16 , simplify right side
9x² + 6x + 1 = 5x² + 18x + 17 ( subtract 5x² + 18x + 17 from both sides )
4x² - 12x - 16 = 0 ( divide through by 4 )
x² - 3x - 4 = 0 ← in standard form
(x - 4)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 1 = 0 ⇒ x = - 1
However, x > 0 thus x = 4
