Let's say the original length of the rectangle is $L$ and the original width is $W$.
The original area of the rectangle is $L \cdot W$.
After increasing the length by $25\%$, the new length of the rectangle is $1.25L$.
Let's say the width of the rectangle is decreased by $x\%$.
The new width of the rectangle is $(1 - \frac{x}{100})W$.
The new area of the rectangle is $(1.25L) \cdot (1 - \frac{x}{100})W$.
Since the area of the rectangle remains unchanged, we have:
$L \cdot W = (1.25L) \cdot (1 - \frac{x}{100})W$
Simplifying the equation, we get:
$1 = 1.25(1 - \frac{x}{100})$
Dividing both sides by $1.25$, we get:
$\frac{4}{5} = 1 - \frac{x}{100}$
Subtracting $1$ from both sides, we get:
$\frac{x}{100} = \frac{1}{5}$
Multiplying both sides by $100$, we get:
$x = 20$
Therefore, the width of the rectangle was decreased by $\boxed{20\%}$.The answer is: 20
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The length of a rectangle is increased by $25\%$, but the width of the rectangle is decreased to keep the area of the rectangle  unchanged.  By what percent was the rectangle's width  decreased?

### Answer:
