Answer
x = 1
Work Step by Step
We will use given data about triangle ABC and Pythagoras Theorem to solve for 'x'-
We know that -
$(\sqrt 10)^{2} =(x+2)^{2} + x^{2}$ ( Pythagoras Theorem)
Therefore -
$10 = (x^{2} + 4 x + 4) + x^{2}$
$10 = 2x^{2} + 4 x + 4 $
$2x^{2} + 4 x - 6 $ = 0
$x^{2} + 2 x - 3 $ = 0
$x^{2} + 3 x -x - 3 $ = 0
$ x (x+3) -1(x+3)$ = 0
$ (x+3) (x-1)$ = 0
Therefore Either x=1 or -3
As x is a length, it can not be negative,
Therefore
x = 1
