The length of a rectangle is 5 inches longer than its width. Its perimeter is 45 inches. Let w equal the width of the rectangle. Write an expression for the length in terms of the width. Use expressions for the length and width to write an equation for the perimeter, on the basis of the given information

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.