Questions: Understanding Perimeter

Question 1

A rectangle has a length of 5 cm and a width of 3 cm. What is its perimeter?

• A. 8 cm — add length plus width
• B. 15 cm — multiply length times width
• C. 16 cm — add all four sides: 5 + 3 + 5 + 3
• D. 5 cm — use only the longest side

Answer: (C)

Perimeter is the total distance around all sides of the shape. A rectangle has two lengths and two widths: 5 + 3 + 5 + 3 = 16 cm. The most common error is adding only one length and one width (getting 8), which counts each pair of sides only once instead of twice. Because opposite sides of a rectangle are equal, you must count each side — both the top and bottom (5 + 5) and both the left and right (3 + 3).

Question 2

A student correctly calculates the perimeter of a 4-foot by 6-foot rectangle as 20, but writes no unit. What is wrong with this answer?

• A. The calculation is wrong — the correct perimeter is 24
• B. The answer is incomplete — perimeter is a distance measurement and must include units (20 feet)
• C. Perimeter should be found by multiplying, not adding
• D. Only two sides need to be added for a rectangle's perimeter

Answer: (B)

Perimeter is a distance — the total length you would walk around the outside of a shape. Distances always require a unit (cm, feet, meters, etc.) to be meaningful. '20' without a unit is like saying 'I walked 20' — 20 what? The calculation 4+6+4+6=20 is correct, but the answer is incomplete without 'feet.' Writing units is not a technicality; it is what makes a measurement answer meaningful and usable.

Question 3

To find the perimeter of a rectangle, you add all four side lengths together.

• T. True
• F. False

Answer: True

Perimeter is the total distance around the outside of a shape — the sum of all side lengths. For a rectangle, that means adding both lengths and both widths. Because opposite sides are equal, this simplifies to length + width + length + width, but the key principle is that all four sides contribute. Counting only two sides gives the perimeter of half the rectangle, not the whole.

Question 4

For a rectangle, you primarily need to add the length and width once (not twice) to find the perimeter, because adding twice would count the shape twice.

• T. True
• F. False

Answer: False

Adding length + width gives only half the perimeter — the distance along two sides. To walk completely around the rectangle, you travel both lengths and both widths. The correct calculation is length + width + length + width (or equivalently, 2 × length + 2 × width). The shortcut 'multiply each side by 2 and add' works precisely because opposite sides are equal, but it still accounts for all four sides.

Question 5

Why does every perimeter answer need to include a unit, and what type of measurement is perimeter?

Model answer: Perimeter is a distance measurement — the total length of the path around the outside of a shape. Distance is always measured in length units (centimeters, feet, meters, etc.). Without a unit, a number like '10' could mean 10 centimeters, 10 feet, or 10 miles — completely different distances. The unit is what makes the measurement meaningful and allows comparison with other measurements.

Requiring units on measurement answers is not bureaucratic formality — it is what makes measurements communicate real-world quantities. This habit becomes increasingly important as students work with area (square units), volume (cubic units), and conversion between unit systems. Establishing the expectation that 'a distance needs a unit' at the perimeter level prevents persistent unitless answers in later measurement work.