Problem 12 · 2013 Math Kangaroo
Hard
Geometry & Measurement
perimeterarithmetic-sequence
The figure shown is made up of six unit squares; its perimeter is 14 cm. Squares are added to this figure in the same zigzag way (alternating bottom-right and top-right) until it is made up of 2013 unit squares. How big is the perimeter of the newly created figure?
Show answer
Answer: B — 4028
Show hints
Hint 1 of 2
Find a simple rule linking the number of squares to the perimeter using the given case (6 squares, 14 cm).
Still stuck? Show hint 2 →
Hint 2 of 2
Each square added to the zigzag adds the same fixed amount to the perimeter.
Show solution
Approach: find the linear perimeter rule, then plug in 2013
- For the staircase of unit squares, the perimeter follows P = 2n + 2 (check: n = 6 gives 2 · 6 + 2 = 14).
- For n = 2013: P = 2 · 2013 + 2 = 4028.
- The new perimeter is 4028.
Mark:
· log in to save