the perimeter of a rectangle is 126 inches. the length exceeds the width

Yep. Where is the rest of the problem?

To find the dimensions of the rectangle, we need to set up an equation using the given information. Let's assume the width of the rectangle is "w" inches. Since the length exceeds the width, the length can be represented as "w + x," where "x" is the amount by which the length exceeds the width.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Using the given information, we can set up the equation:

126 = 2(w + (w + x))

Simplifying the equation:

126 = 2(2w + x)
63 = 2w + x

Now we have two variables, which means we need one more equation to solve for both x and w. However, we know that the length exceeds the width, so we can assume x is a positive value.

Let's consider some possible values for x and calculate the corresponding value of w:

If x = 1, then w = (63 - 2(1))/2 = 30.5
If x = 2, then w = (63 - 2(2))/2 = 29.5
If x = 3, then w = (63 - 2(3))/2 = 28.5

We can see a pattern here. As x increases by 1, w decreases by 1. This indicates that x represents the number of units that the length exceeds the width.

So, the dimensions of the rectangle are:
Length = w + x = w + (w + x) = 2w + x
Width = w

Therefore, we have:
Length = 2w + x
Width = w

For any positive value of x, the length can be expressed as 2w + x, and the width is simply w.