The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x - 1) cm and (x + 3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:

The correct answer is 10.

To find the hypotenuse of the right-angled triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let the three sides of the right-angled triangle be:
Leg 1: $a=x-1$
Leg 2: $b=x+1$
Hypotenuse: $c=x+3$

According to the Pythagorean theorem:
$a^2+b^2=c^2$

Substitute the expressions for the sides into the equation:
${(x-1)}^2+{(x+1)}^2={(x+3)}^2$

Expand each term:
$(x^2-2x+1)+(x^2+2x+1)=x^2+6x+9$

Combine like terms on the left side of the equation:
$2x^2+2=x^2+6x+9$

Rearrange the terms to form a standard quadratic equation:
$x^2-6x-7=0$

Factor the quadratic equation:
$(x-7)(x+1)=0$

This gives two possible values for $x$:
$x=7$ or $x=-1$

Since the sides of a triangle must have positive lengths, $x$ must be positive. Therefore:
$x=7$

Now, calculate the length of the hypotenuse:
Hypotenuse $=x+3=7+3=10$ cm