Answer
x = 4
Work Step by Step
We will use given data about triangle ABC and Pythagoras Theorem to solve for 'x'-
We know that -
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
$5^{2} =(x)^{2} + (x-1)^{2}$
Therefore -
$25 = x^{2} + (x^{2} - 2x +1)$
$25 = 2x^{2} - 2 x + 1 $
$2x^{2} - 2 x - 24 $ = 0
$x^{2} - x - 12 $ = 0
$x^{2} + 3 x -4x - 12 $ = 0
$ x (x+3) -4(x+3)$ = 0
$ (x+3) (x-4)$ = 0
Therefore Either x = 4 or -3
As x is a length, it can not be negative,
Therefore
x = 4
