Let's denote the length of the rectangle by $L$ and the width by $W$. Since the length and width are consecutive integers, we can express them as:

$L = W + 1$

The formula for the perimeter $P$ of a rectangle is given by:

$P = 2(L + W)$

We know the perimeter is 86 inches:

$2(L + W) = 86$

Now, substitute $L = W + 1$ into the perimeter equation:

$2((W + 1) + W) = 86$

Simplify the equation:

$2(2W + 1) = 86$

Divide both sides by 2:

$2W + 1 = 43$

Subtract 1 from both sides:

$2W = 42$

Finally, divide by 2:

$W = 21$

Since $L = W + 1$:

$L = 21 + 1 = 22$

So, the length is 22 inches, and the width is 21 inches.

Summary:

• Length: 22 inches
• Width: 21 inches

Would you like a detailed explanation or have any other questions?

Here are five related questions:

1. What is the area of this rectangle?
2. How would the perimeter change if the length and width were both increased by 2 inches?
3. If the width were doubled, what would be the new perimeter?
4. What would the perimeter be if the length and width were both decreased by 3 inches?
5. Can you find another pair of consecutive integers that would give a different perimeter?

Tip: Remember, for any two consecutive integers, if you know one, you can always find the other by adding or subtracting 1.