Perimeter of a Rectangle

Statement

The perimeter of a rectangle is the total distance around it. Since a rectangle has two lengths and two widths, the perimeter formula is:

\[ P = 2(\ell + w) \]

Here, \(\ell\) is the length and \(w\) is the width.

Why it’s true

• The rectangle has two pairs of equal sides: two lengths and two widths.
• Adding them gives \(P = \ell + w + \ell + w = 2\ell + 2w\).
• This can be factored into \(P = 2(\ell + w)\).

Recipe (how to use it)

1. Identify the length (\(\ell\)) and width (\(w\)).
2. Add them together: \(\ell + w\).
3. Multiply the result by 2 to get the perimeter.

Spotting it

Any time you are asked to find the total boundary length of a rectangle or a square, use this formula.

Common pairings

• Word problems about fencing a rectangular field.
• Comparing perimeters of different rectangles.
• Combined with area calculations.

Mini examples

1. Given: Length = 8, Width = 5. Find: Perimeter. Answer: \(P = 2(8+5) = 26\).
2. Given: Length = 12, Width = 7. Find: Perimeter. Answer: \(P = 2(12+7) = 38\).

Pitfalls

• Forgetting to multiply by 2 after adding length and width.
• Mixing up perimeter with area (\(A = \ell \times w\)).

Exam strategy

• Always label length and width clearly in word problems.
• Write out the sum first before multiplying by 2.
• If only perimeter and one side are given, rearrange formula to solve for the other side.

Summary

The perimeter of a rectangle is given by \(P=2(\ell+w)\). It represents the distance around the shape. Remember: add length and width, then double.