Math, asked by saranshthakur80, 9 months ago

What is Pythagorean triplet​

Answers

Answered by venillaraj999
2

Answer:

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.

Answered by shouryarawat
1

Answer:

A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:

a2 + b2 = c2

Example: The smallest Pythagorean Triple is 3, 4 and 5.

Let's check it:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

Yes, it is a Pythagorean Triple!

Triangles

Pythagoras

When a triangle's sides are a Pythagorean Triple it is a right angled triangle.

pythagoras squares  a^2 + b^2 = c^2

See Pythagoras' Theorem for more details.

Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle:

triangle 3 4 5  

triangle 3 4 5 lego

 

Here are two more Pythagorean Triples:

5, 12, 13   9, 40, 41

     

5, 12, 13 Triangle   9, 40, 41 Triangle

52 + 122 = 132   92 + 402 = 412

25 + 144 = 169   (try it yourself)

 

And each triangle has a right angle!

List of the First Few

Here is a list of the first few Pythagorean Triples (not including "scaled up" versions mentioned below):

(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17)

(9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)

(15,112,113) (16, 63, 65) (17,144,145) (19,180,181)

(20, 21, 29) (20, 99,101) (21,220,221) (23,264,265)

(24,143,145) (25,312,313) (27,364,365) (28, 45, 53)

(28,195,197) (29,420,421) (31,480,481) (32,255,257)

(33, 56, 65) (33,544,545) (35,612,613) (36, 77, 85)

(36,323,325) (37,684,685) ... infinitely many more ...

Scale Them Up

The simplest way to create further Pythagorean Triples is to scale up a set of triples.

Example: scale 3, 4, 5 by 2 gives 6, 8, 10

Which also fits the formula a2 + b2 = c2:

62 + 82 = 102

36 + 64 = 100

If you want to know more about them read Pythagorean Triples - Advanced

 

Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10  

Pythagoras Theorem

Right Angled triangles

Pythagorean Triples - Advanced

Triangles

Proof that a Triangle has 180°

Step-by-step explanation:

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