To find the width of the rectangle, we can use the formula for the perimeter of a rectangle. The perimeter (P) of a rectangle is the sum of twice its length (L) and twice its width (W).
The formula for the perimeter of a rectangle is given by:
[tex]\[ P = 2L + 2W \][/tex]
In this question, we are given that the perimeter (P) is 120 cm and the length (L) is 45 cm. We need to solve for the width (W).
First, we can write down the given perimeter formula with the provided values:
[tex]\[ 120 = 2(45) + 2W \][/tex]
Now, let's solve for W step by step:
1. Multiply the length by 2:
[tex]\[ 120 = 90 + 2W \][/tex]
2. Subtract 90 from both sides of the equation to isolate the term with W:
[tex]\[ 120 - 90 = 2W \][/tex]
3. This simplifies to:
[tex]\[ 30 = 2W \][/tex]
4. Finally, divide both sides by 2 to solve for the width:
[tex]\[ \frac{30}{2} = W \][/tex]
[tex]\[ W = 15 \][/tex]
So the width of the rectangle is 15 cm.
