The perimeter of the rectangle is 114 dm and its width is 9 dm less than the length. find the sides of the rectangle.

1. To solve the problem, recall the formula for finding the perimeter: P = 2 * (a + b), where a and b are the sides of the rectangle.

2. Let the width be “x”, then the length is “x + 9”.

3. Substitute the obtained value into the perimeter formula and obtain the following equation:

P = 2 * (a + b);
114 = 2 * (x + (x + 9)).

4. Let’s solve the resulting equation:

2 * (x + (x + 9)) = 114;
x + (x + 9) = 114: 2;
x + x + 9 = 57;
2x + 9 = 57;
2x = 57 – 9;
2x = 48;
x = 48: 2;
x = 24.

5. We get that the width is 24 dm, and the length is 24 + 9 = 33 dm.

Answer: 24 dm; 33 dm.