Theory:
The resistance of a wire depends on its length, cross-sectional area, and resistivity. When a wire is stretched, its length increases, and as a result, its resistance also changes. The change in resistance can be calculated using the formula:

Percentage change in resistance = (Change in resistance / Initial resistance) x 100%

Given:
Resistance of wire before stretching = R
Percentage increase in length = 50%

Calculation:

1. Change in length:
Let's assume the initial length of the wire is L. When it is stretched by 50%, the change in length can be calculated as:
Change in length = (50/100) x L = 0.5L

2. Change in resistance:
The resistance of a wire is directly proportional to its length. Therefore, the change in resistance can be calculated as:
Change in resistance = (Change in length / Initial length) x Initial resistance
Change in resistance = (0.5L / L) x R = 0.5R

3. Percentage change in resistance:
To find the percentage change in resistance, we will use the formula mentioned earlier:
Percentage change in resistance = (Change in resistance / Initial resistance) x 100%
Percentage change in resistance = (0.5R / R) x 100% = 50%

Conclusion:
The percentage change in the resistance of the wire when it is stretched by 50% is 50%. This means that the resistance of the wire increases by 50% due to the increase in its length.