Let the shorter leg = x
shorter leg =x
longer leg = 2x + 4
hypotenuse = 3x - 4
Given that a² + b² = c²
x² + (2x + 4)² = (3x - 4)²
Remove brackets : (a + b)² = a² + 2ab + b²:
x² + 4x² + 16x + 16 = 9x² - 24x + 16
Moved all terms to the left:
x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0
Combine like terms:
-5x² + 40x = 0
Multiply all terms by -1:
5x² - 40x = 0
Take out 5x as common factor:
5x(x - 8) = 0
Apply zero product property:
5x = 0 or x - 8 = 0
Evaluate:
x = 0 or x = 8
Since length cannot be zero, shorter leg = 8
shorter leg = 8
Hypotenuse = 3(8) - 4 = 20
Answer: 20 units