The length of the rectangle was increased by 6 dm and the width decreased by 4 dm. How the perimeter has changed.

Let’s write the formula for the perimeter of a rectangle:

P = 2 * (a + b), where a and b are the sides of the rectangle.

Let’s write down the known data:

Since the length of the rectangle was increased by 6 dm, then after the change the length of the rectangle will be equal to a + 6 dm;
Since the width of the rectangle was reduced by 4 dm, then after the change the width of the rectangle will be equal to b – 4 dm;
We got a new rectangle with sides a + 6 and b – 4.
In order to find the perimeter of a rectangle, you need to substitute the known values ​​into the formula for the perimeter of a rectangle and calculate its value. That is, we get:

P = 2 * ((a + 6) + (b – 4));

First, we open the brackets. If there is a minus sign in front of the brackets, then when it is expanded, the signs of the values ​​are changed to the opposite sign. If there is a plus sign in front of the brackets, then when it is expanded, the value signs remain unchanged. That is, we get:

P = 2 * ((a + 6) + (b – 4)) = 2 * (a + 6 + b – 4) = 2 * (a + b + 2);

Find the change in the perimeter after changing the sides of the rectangle
In order to find the change in the perimeter of the rectangle, you need to subtract the perimeter of the rectangle before changing the perimeter of the new rectangle with the changed sides. That is, we get:

2 * (a + b + 2) – 2 * (a + b);

We open the brackets. To do this, the value in front of the brackets, we multiply by each value in the brackets, and add them in accordance with their signs. Then we get:

2 * (a + b + 2) – 2 * (a + b) = 2 * a + 2 * b + 2 * 2 – 2 * a – 2 * b = 2 * a + 2 * b + 4 – 2 * a – 2 * b = 4.

Hence, we find that the perimeter with the changed sides will increase by 4 dm.