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Pythagorean Distance

Pythagorean Distance problems involve finding the shortest distance between two points when the path consists of perpendicular movements (North-South and East-West). The straight-line distance is the hypotenuse of the right triangle formed by the two perpendicular legs.

10Worksheets
200+Practice Questions
IntermediateDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Pythagorean Distance

Pythagorean Distance problems involve finding the shortest distance between two points when the path consists of perpendicular movements (North-South and East-West). The straight-line distance is the hypotenuse of the right triangle formed by the two perpendicular legs.

Prerequisites

Pythagorean theorem: a² + b² = c² Right angle concept Square root calculation Recognition of Pythagorean triplets
Why This Matters: Pythagorean Distance problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test application of the Pythagorean theorem in direction sense contexts.

How to Solve Pythagorean Distance Problems

1

Step 1: Identify the two perpendicular movements (e.g., North then East)

2

Step 2: Let a = first distance, b = second distance

3

Step 3: Apply Pythagorean theorem: c = √(a² + b²)

4

Step 4: Calculate the square root

5

Step 5: Round to nearest integer if needed

6

Step 6: Answer with the shortest distance

Pro Strategy: Recognize Pythagorean triplets (3-4-5, 5-12-13, 8-15-17, 7-24-25) for quick calculation. If numbers are not triplets, use the square root formula.

Example Problem

Example: A person walks 3 km East, then 4 km North. What is the shortest distance from start? Solution: Step 1: Movements are East (3 km) and North (4 km) → perpendicular Step 2: a = 3, b = 4 Step 3: c = √(3² + 4²) = √(9 + 16) = √25 = 5 km Answer: 5 km

Pro Tips & Tricks

  • Common Pythagorean triplets: (3,4,5), (5,12,13), (8,15,17), (7,24,25), (9,40,41)
  • If legs are given, hypotenuse = √(a² + b²)
  • If hypotenuse and one leg are given, other leg = √(c² - a²)
  • Directions that are perpendicular: North & East, North & West, South & East, South & West

Shortcut Methods to Solve Faster

For triplet (3,4,5): distance = 5k where k is scaling factor
For triplet (5,12,13): distance = 13k
For triplet (8,15,17): distance = 17k

Common Mistakes to Avoid

Using Pythagoras when movements are not perpendicular
Forgetting to take square root
Adding legs instead of squaring them

Exam Importance

Pythagorean Distance is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Pythagorean Distance?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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