Correct Answer: 1 cm

Solution : Let $a$ and $b$ be the two sides other than the hypotenuse.
Use the Pythagoras theorem: Hypotenuse ² = Base ² + Perpendicular ²
According to the question,
$(29)^{2} = a^{2} + b^{2}$
⇒ 841 = $a^{2} + b^{2}$
Also, $a +  b$ = 41
⇒ $a = 41 – b$
Now,
⇒  $(41−b)^{2} + b^{2} = 841$
⇒ $1681 − 82b + 2b^{2}$ = 841
⇒ $2b^{2} − 82b + 840$ = 0
⇒ $b^{2} − 41b + 420$ = 0
⇒ $(b − 20)(b − 21)$ = 0
If $b$ = 20, then
⇒ $a$ = 41– 20 = 21
If $b$ = 21, then
⇒ $a$ = 41– 21 = 20
The difference between the two sides is (|a – b|) = |20 – 21| = 1
Hence, the correct answer is 1 cm.