Find the perimeter of squares with sides 1 cm, 1.5 cm, 2 cm, 2.5 cm and 3 cm. What will happen to the perimeters if the sides increase by 0.5 cm?
Answer: Perimeters: 4 cm, 6 cm, 8 cm, 10 cm, 12 cm. Each time the side increases by 0.5 cm, the perimeter increases by 2 cm.
Step-by-step solution
Idea: Perimeter = 4 × side. If the side grows by 0.5 cm, the perimeter grows by 4 × 0.5 = 2 cm, every time.
- Use perimeter = 4x:1 mark
Side x (cm) 1 1.5 2 2.5 3 Perimeter 4x (cm) 4 6 8 10 12 - Differences: 6 − 4 = 2, 8 − 6 = 2, 10 − 8 = 2, 12 − 10 = 2. Each increase of 0.5 cm in the side increases the perimeter by 2 cm.½ mark
- Reason: new perimeter = 4(x + 0.5) = 4x + 2. The increase is always 2 cm, whatever the side. A constant difference like this is the mark of a linear pattern.½ mark
The perimeters are 4 cm, 6 cm, 8 cm, 10 cm and 12 cm; each 0.5 cm increase in the side increases the perimeter by 2 cm.
Answer to write in the exam
Perimeter = 4 × side
Sides 1, 1.5, 2, 2.5, 3 cm → perimeters 4, 6, 8, 10, 12 cm
4(x + 0.5) − 4x = 2
∴ Each increase of 0.5 cm in the side increases the perimeter by 2 cm
Common mistakes that cost marks
- Saying the perimeter also increases by 0.5 cm. All four sides grow, so it increases by 4 × 0.5 = 2 cm.
- Squaring the side (finding the area: 1, 2.25, 4, …) instead of finding the perimeter.
- Giving the five perimeters but not answering the second question: say that each 0.5 cm increase in the side increases the perimeter by 2 cm.
How this can come in the exam
MCQ (1 mark)
The side of a square increases from 3.5 cm to 4 cm. Its perimeter increases by
- 0.5 cm
- 1 cm
- 2 cm
- 4 cm
Show answer
(C) 2 cm
4 × 0.5 = 2 cm.
Short answer (2 marks)
The sides of equilateral triangles are 2 cm, 2.5 cm, 3 cm and 3.5 cm. Find their perimeters and the constant increase.
Show answer
Perimeter = 3 × side: 6, 7.5, 9, 10.5 cm (1 mark). Each step increases the perimeter by 3 × 0.5 = 1.5 cm (1 mark).Try one yourself
Find the perimeters of squares with sides 4 cm, 4.25 cm, 4.5 cm and 4.75 cm. By how much does the perimeter grow each time?
Show answer
16, 17, 18, 19 cm. It grows by 4 × 0.25 = 1 cm each time.
More questions like this
- A chess club charges a joining fee of ₹200 plus ₹50 for every match played. The following table shows the amount a player will have to pay as the number of matches varies.
- A chess club charges a joining fee of ₹200 plus ₹50 for every match played. If a player paid ₹750, how many matches did he play?
- The sum of two numbers is 64. One of the numbers is 10 more than the other. What are the two numbers?
- We have learnt that to evaluate the value of an algebraic expression, we substitute a value of the variable in the given expression. Consider the example where the wire is bent to form a rectangle. Here, the area of the rectangle, 10x − x2, is a function of x. Can you interpret this as an input-output process? What value does the expression take when x = 6 cm?
- Find the value of the linear polynomial 5x − 3 if: