Answer:
13 units.
Step-by-step explanation:
By Pythagoras:
(x -3)^2 + (x + 4)^2 = (2x - 3)^2
x^2 - 6x + 9 + x^2 + 8x + 16 = 4x^2 -12x + 9
4x^2 - x^2 - x^2 + 6x - 8x - 12x + 9 - 9 - 16 = 0
2x^2 -14x - 16 = 0
2(x^2 - 7x - 8) = 0
2(x -8)(x + 1) =0
x = 8, -1.
As x must be positive we take x = 8
So the hypotenuse is 2(8) - 3 = 13 units long.
