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To write an expression for the length in terms of the width, we can use the given information that the length of the rectangle is 5 inches longer than its width. Let's use the variable "w" to represent the width:
Length = Width + 5 = w + 5
To write an equation for the perimeter, we need to consider that the perimeter is the sum of all the sides of the rectangle. For a rectangle, the perimeter is given by the formula:
Perimeter = 2 * (Length + Width)
Substituting the expressions for length and width, we can write the equation for the perimeter as:
Perimeter = 2 * (w + 5 + w)
Simplifying the equation, we get:
Perimeter = 2w + 10 + 2w
Perimeter = 4w + 10
Since the problem states that the perimeter is 45 inches, we can set the equation equal to 45:
4w + 10 = 45
Now, we can solve this equation to find the value of w, which represents the width of the rectangle.