If you know the perimeter and all the sides but one, you can find the missing side. It is a missing-number problem, like the ones you solved with a letter for the unknown.
Why it works
The perimeter is all the sides added together. So the sides you know plus the missing side make the perimeter. Taking the known sides away from the perimeter leaves exactly the missing side. For a rectangle, use what you know about its shape: the two lengths are equal and the two widths are equal.
Key idea
Missing side = perimeter $-$ the sum of the sides you know. In a rectangle, take away both lengths, then split what is left into the two equal widths.
Worked example: Any polygon
A shape has sides of 5, 5 and 11 cm and one unknown side. Its perimeter is 26 cm. Find the unknown side.
- Known sides: $5 + 5 + 11 = 21$.
- $26 - 21 = 5$.
- Check: $5 + 5 + 5 + 11 = 26$.
Answer: 5 cm
Worked example: A rectangle
A rectangle has a perimeter of 30 m and a length of 9 m. What is its width?
- Two lengths: $9 + 9 = 18$.
- Two widths make the rest: $30 - 18 = 12$.
- Each width: $12 \div 2 = 6$.
- Check: $9 + 6 + 9 + 6 = 30$.
Answer: 6 m
Worked example: A square
A square has a perimeter of 28 in. How long is each side?
- 4 equal sides: $4 \times \square = 28$.
- $28 \div 4 = 7$.
Answer: 7 in
Common mistake
Forgetting that a rectangle has two lengths. $30 - 9 = 21$ is not the width. The perimeter goes around both lengths and both widths. Check your answer by adding all four sides.