Pythagorean Triples, a fundamental concept in mathematics, have a significant role in competitive exams in India such as SSC CGL, CHSL, MTS, Banking Exams, AFCAT, UPSC, and others.
This article aims to shed light on the importance of Pythagorean Triples, explain the concept in detail, list all the Pythagorean Triples up to 50, and provide tips on how to prepare for these exams.
Competitive exams in India often test candidates' speed and accuracy in solving problems. Pythagorean Triples come into play in various sections of these exams, especially in Quantitative Aptitude and Reasoning.
Understanding Pythagorean Triples can help candidates solve problems related to triangles, distances, and arrangements more quickly and accurately, saving valuable time during the exam.
Understanding Pythagorean Triples
A Pythagorean Triple consists of three positive integers a, b, and c, such that $$a^2 + b^2 = c^2$$
In other words, they form the sides of a right-angled triangle, with 'c' being the hypotenuse. The most common example is (3, 4, 5).
Pythagorean Triples are not only academically interesting but also practically useful in various fields, including competitive exams.
Pythagorean Triples Up To 50
Here are all the Pythagorean Triples where all sides are less than or equal to 50:
| (3, 4, 5) | (5, 12, 13) | (6, 8, 10) | (7, 24, 25) |
| (8, 15, 17) | (9, 12, 15) | (9, 40, 41) | (10, 24, 26) |
| (12, 16, 20) | (12, 35, 37) | (14, 48, 50) | (15, 20, 25) |
| (15, 36, 39) | (16, 30, 34) | (18, 24, 30) | (20, 21, 29) |
| (21, 28, 35) | (24, 32, 40) | (27, 36, 45) | (30, 40, 50) |
Incase you want to see them in form of equations, then you check the following:
- $$3^2 + 4^2 = 5^2$$
- $$5^2 + 12^2 = 13^2$$
- $$6^2 + 8^2 = 10^2$$
- $$7^2 + 24^2 = 25^2$$
- $$8^2 + 15^2 = 17^2$$
- $$9^2 + 12^2 = 15^2$$
- $$9^2 + 40^2 = 41^2$$
- $$10^2 + 24^2 = 26^2$$
- $$12^2 + 16^2 = 20^2$$
- $$12^2 + 35^2 = 37^2$$
- $$14^2 + 48^2 = 50^2$$
- $$15^2 + 20^2 = 25^2$$
- $$15^2 + 36^2 = 39^2$$
- $$16^2 + 30^2 = 34^2$$
- $$18^2 + 24^2 = 30^2$$
- $$20^2 + 21^2 = 29^2$$
- $$21^2 + 28^2 = 35^2$$
- $$24^2 + 32^2 = 40^2$$
- $$27^2 + 36^2 = 45^2$$
- $$30^2 + 40^2 = 50^2$$
Preparing Pythagorean Triples for Competitive Exams
To prepare Pythagorean Triples for competitive exams, start by understanding the concept and then memorize the triples up to a reasonable limit, such as 50. Regular practice is key. Try to incorporate these triples in solving different types of problems. Over time, you'll find that recognizing these triples can significantly speed up your problem-solving process.
Conclusion
Understanding and memorizing Pythagorean Triples can give you an edge in competitive exams. It's a simple yet powerful tool that can help you solve problems more efficiently. So, embrace the power of Pythagorean Triples and let it be your stepping stone to success in competitive exams.
Success is the sum of small efforts, repeated day in and day out.