The length of the three sides of a right angled triangle are (x - 2) cm, (x) cm and (x + 2) cm respectively. Then the value of x is

According to question,
ABC is a right angle triangle

∴ Apply Pythagoras theorem
AC² = AB² +BC²
(x + 2)² = (x - 2)² + x²
x² + 4 + 4x = x² + 4 - 4x + x²
x² = 8x
x = 8

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Alternate : From option approach
$$\eqalign{ & \left( {x - 2} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {x + 2} \right) \cr & \,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \cr & \,\,\,\,\,\,\,6\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Triplet}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{x}} = {\text{8}} \cr} $$