Problem 5 · 2017 Math Kangaroo
Easy
Geometry & Measurement
perimeter
The diagram shows two rectangles whose sides are parallel to each other. By how much is the perimeter of the bigger rectangle greater than the perimeter of the smaller rectangle?
Show answer
Answer: E — 24 m
Show hints
Hint 1 of 2
Perimeter depends only on width plus height, doubled — where the smaller rectangle sits doesn't matter.
Still stuck? Show hint 2 →
Hint 2 of 2
Find each rectangle's width and height from the labelled pieces.
Show solution
Approach: compare total width+height of each rectangle
- Perimeter = 2 × (width + height), so only how much wider and taller the big rectangle is matters, not where the small one sits.
- The labelled gaps show the big rectangle is wider by 2 m + 4 m = 6 m and taller by 3 m + 3 m = 6 m, a total extra of 12 m in width-plus-height.
- The perimeter difference is twice that: 2 × 12 = 24 m.
Mark:
· log in to save