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All courses Math Foundations · MF.GM.2 49 of 60
Find and interpret perimeter and circumference in numeric and contextual problems.

Add the side lengths for perimeter

Problem
A rectangle has side lengths 8 cm and 5 cm. What is its perimeter?
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Hint

Start by listing every outside side of the rectangle once. A rectangle has two 8 cm sides and two 5 cm sides.

Perimeter means the total distance around the outside of the shape, so add all four side lengths, not 8 × 5.

Solution walkthrough

01

Identify every outer side of the rectangle

\[\text{Sides}:~8~\text{cm},~5~\text{cm},~8~\text{cm},~5~\text{cm}\]

A rectangle has two sides of each length. For perimeter, you go all the way around the outside, so both 8 cm sides and both 5 cm sides must be counted.

02

Write the perimeter sum

\[P~=~8~+~5~+~8~+~5\]

Perimeter means total distance around the shape, so add all four side lengths once.

03

Add the side lengths

\[P~=~13~+~13~=~26\]

First add one length and one width: 8 + 5 = 13. The other pair is the same, so the total is 13 + 13 = 26.

04

State the perimeter with units

\[P~=~26~\text{cm}\]

The problem asks for perimeter, so the answer is a length measurement in centimeters.

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Another way

  1. Use the rectangle shortcut: P = 2(8 + 5) = 2(13) = 26 cm.

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Common mistake

Adding only 8 + 5 = 13 and stopping. That counts just two sides, but a rectangle has four outer sides, so both opposite sides must be included.