The bisector of one of the angles of a rectangle also bisects a side of the rectangle. Find the perimeter of the rectangle if you know that the shorter side of the rectangle is equal to 10 cm.
Let's call the longer side of the rectangle $x$. Since the shorter side is 10 cm, we know that the longer side is equal to $x$.
Let's draw a diagram to help visualize the problem:
```
_______________ ________
| |
| |
| x |
|------ -----|
10
```
The bisector of one of the angles of the rectangle cuts the longer side into two equal parts. So each part is of length $\frac{x}{2}$.
We can also see that the two parts together must add up to the longer side, which is $x$.
Therefore, we can set up the equation:
$\frac{x}{2} + \frac{x}{2} = x$
Simplifying, we find:
$x = \frac{x}{2} + \frac{x}{2}$
$2x = x + x$
$2x = 2x$
Since the right side and left side of the equation are equal, we know that this equation is true for any value of $x$. Therefore, we can say that the equation is true where $x = 10$.
Now, we can find the perimeter of the rectangle.
The perimeter is the sum of all four sides of the rectangle.
$P = 2 \times (\text{length} + \text{width})$
$P = 2 \times (10 + x)$
$P = 2 \times (10 + 10)$
$P = 2 \times 20$
$P = 40$
Therefore, the perimeter of the rectangle is 40 cm.