Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78.

Set up an equation involving only L, the length of the rectangle.

Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Lenght Width

Let w be the width of the rectangle.

L = w + 3
(L - 3 = w)

2L + 2w = 78
2L + 2(L-3) = 78
2L + 2L - 6 = 78
4L = 84
L = 21 in.

W = L - 3 = 21 - 3 = 18 in.

To set up an equation involving only the length (L) of the rectangle, we can use the given information that the length is 3 inches longer than the width.

Let's assume the width of the rectangle is represented by 'W'.

According to the given information, the length (L) of the rectangle is equal to the width (W) plus 3 inches. So, we can write:

L = W + 3

To find the value of the length of the rectangle, we also need to use the information that the perimeter of the rectangle is 78 inches.

The formula for the perimeter of a rectangle is: Perimeter = 2 * (Length + Width)

Substituting the values into the formula, we get:

78 = 2 * (L + W)

Since we want to express the equation in terms of L only, we can substitute the value of L from the first equation into the second equation:

78 = 2 * ((W + 3) + W)

Now, we can simplify the equation:

78 = 2 * (2W + 3)

Divide both sides of the equation by 2:

39 = 2W + 3

Subtract 3 from both sides:

36 = 2W

Divide both sides by 2:

18 = W

Therefore, the width of the rectangle is 18 inches.

To find the length (L), we can substitute the value of W into the first equation:

L = W + 3
L = 18 + 3
L = 21

Therefore, the length of the rectangle is 21 inches.