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.

Answer 1

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.