Growing Squares
Growing Squares problems feature concentric or nested squares that increase in size at each step. The side length may increase by a constant amount (arithmetic progression) or by a constant ratio (geometric progression). You must calculate the next square's size.
What You'll Learn
Introduction to Growing Squares
Growing Squares problems feature concentric or nested squares that increase in size at each step. The side length may increase by a constant amount (arithmetic progression) or by a constant ratio (geometric progression). You must calculate the next square's size.
Prerequisites
How to Solve Growing Squares Problems
Step 1: Measure the side length of each square
Step 2: Calculate the difference between consecutive sizes
Step 3: If differences are constant → arithmetic progression
Step 4: If ratios are constant → geometric progression
Step 5: Apply the same change to the last square's size
Step 6: The square is typically centered (concentric)
Step 7: Select the square with the correct size
Example Problem
Example: Square side lengths: 20, 30, 40, 50. What is next side length? Solution: Step 1: Side lengths: 20, 30, 40, 50 Step 2: Differences: +10 each step Step 3: Next side length = 50 + 10 = 60 Answer: Square with side length 60
Pro Tips & Tricks
- Practice regularly to build speed and accuracy
- Understand the concept before memorizing formulas
- Start with easier problems and gradually increase difficulty
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Growing Squares. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Growing Squares is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Growing Squares?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: