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In these lessons, we will learn
- Pythagorean Triples
- Families of Pythagorean Triples
- Pythagorean Triples and Right Triangles
- Solving Problems using the Pythagorean Triples
- How to generate Pythagorean Triples
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Pythagorean Triples
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Pythagorean triples are formed by positive integers a, b and c, such that a2 + b2 = c2. We may write the triple as (a, b, c)
For example, the numbers 3, 4 and 5 form a Pythagorean Triple because 32 + 42 = 52. There are infinitely many Pythagorean triples.
Some examples are ( 3 , 4 , 5 ) | ( 5, 12, 13) | ( 7, 24, 25) | ( 8, 15, 17) |
( 9, 40, 41) | (11, 60, 61) | (12, 35, 37) | (13, 84, 85) |
(16, 63, 65) | (20, 21, 29) | (28, 45, 53) | (33, 56, 65) |
(36, 77, 85) | (39, 80, 89) | (48, 55, 73) | (65, 72, 97) |
Families of Pythagorean Triples
If we multiply each number of a Pythagorean triple by the same number, we form another Pythagorean triple.
For example, (6, 8, 10) is a family of the Pythagorean triple (3, 4, 5) because it can be obtained by 2 × 3 = 6, 2 × 4 = 8, 2 × 5 = 10. If we multiply (3, 4, 5) by 3, we get another triple (9, 12, 15). This can be repeated with different multiples.
Similarly, the family for (5, 12, 13) would be (10, 24, 26), (15, 36, 39) and so on.
Pythagorean Triples and Right Triangles
When we make a triangle with sides whose lengths are the Pythagorean Triples, the triangle will form a right triangle. This follows from the converse of the Pythagorean Theorem.
The following diagram shows some examples of Pythagorean Triples. Scroll down the page for more examples and solutions on Pythagorean Triples and Right Triangles.
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Memorizing some common Pythagorean triples can helpful.
For example, if we see that the sides of a triangle form a Pythagorean triple then we know that it is a right triangle.
The following video gives some examples of Pythagorean triples and right triangles. Any group of 3 integer values that satisfies the equation a2 + b2 = c2 is called a Pythagorean Triple. Therefore, any triangle that has sides that form a Pythagorean Triple must be a right triangle.
- Show Step-by-step Solutions
Solving problems using the Pythagorean Triples
Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem.
Example:
Find the value of x
Solution:
Check for Pythagorean triple:
Get the ratio of the two given sides:
Master of typing 3 5 5 download free. 12 : 20 = 3 : 5 ( divide by 4 )
From the ratio, we know that it is a Pythagorean triple.
So, x = 4 × 4 = 16 cm
The following videos show how to solve some GMAT, SAT and ACT questions using the Pythagorean Triples- Show Step-by-step Solutions
How to generate Pythagorean Triples
The following video will show you how to use an ordinary multiplication table to list infinitely many different examples of Pythagorean TriplesTry the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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Michal founded the company in 2012, after working with large retailers and recognizing the gap between consumers and what companies have to offer them in eCom & data. Prior to that, she was Senior VP in Comme-il-faut (fashion retail), VP business development in Gitam BBDO, and VP media in Gitam BBDO. Michal’s passion is running, Yoga and eCommerce
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Eran is a creative business entrepreneur. In his previous roles Eran established and managed the digital and erCommerce department in Kimberly Clark Israel and was Kimberly Clark’s eCommerce Director for the EMEA region. Earlier in his career, Eran established the digital activity of TBWA Israel and prior to that he managed major multi-sector accounts in several leading advertising agencies: McCann Ericson, BBDO and Ogilvy. In his spare time he is an amateur chef and swimmer. He is married with three boys and lives in Herzlia, Israel
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Doyourdata super eraser 5 7 – secure deletion of data. Erez is a Data Analytics and Data Science expert. In his previous role Erez has worked at Strauss Group as the Big Data and Analytics manager & developed infrastructure and methodologies for extraction of business value from consumer and sales data. Prior to that Erez has worked for Coca-Cola, Yahoo!, Super-Pharm and CAL and held various Analytics and Market Research positions. Erez is very passionate about data and also serves as a lecturer at the Academic Tel-Aviv College
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A professional online shopper that decided to make the obsession her profession.
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With seven years of experience in Wholesale business, she acquired commercial and marketing knowledge. as a brand manager in Luxottica, the biggest eyewear company in the world, she led the marketing strategy of international brands. Florina is passionate about fashion, branding, lifestyle and adopting new digital trends, she’s multitasking, and always looking for a creative solution.
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Adi has been living and breathing digital, advertising and branding for the past 10 years.
Managing Projects and people from birth ?. Nothing escapes her eyes, building processes is her bread and butter. In the last 10 years, Adi had her own digital and branding firm, building strategy, digital marketing plans and project management. She loves working with people, passionate about exploring new areas and learning something new every day.
Managing Projects and people from birth ?. Nothing escapes her eyes, building processes is her bread and butter. In the last 10 years, Adi had her own digital and branding firm, building strategy, digital marketing plans and project management. She loves working with people, passionate about exploring new areas and learning something new every day.
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