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A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. … The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.
A Pythagorean triplet consists of three positive integers a, b, and c, such that a2 + b2 = c2.
Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle
Formula
To find the Pythagorean triples, the following formula is used. If a, b are two sides of the triangle and c is the hypotenuse, then, a, b, and c can be found out using this-
[tex]a \: = {m}^{2} – {n}^{2} [/tex]
[tex]b = 2mn[/tex]
[tex]c = { \: m}^{2} + {n}^{2} [/tex]
These values result in a right-angled triangle with sides a, b, c.
Notes:
(i) m, n and k are any two positive integers
(ii) m > n
(iii) m and n are coprime and both should not be odd numbers
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. … The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.
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Answer:
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Formula
Notes:
Solves Example
Question:
Solution:
Given,
So, (7, 24, 25) is a Pythagorean triple
Kuch reh gya to puch fr
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