Question

state Pythagoras theorem and define Pythagorean triplet. finding a number which is a part of two Pythagorean triplets and finding two triplets which satisfies Pythagoras theorem but is not of the form of Pythagorean triplet​

Answer 1

Answer:

in the right angled triangle the square of hyptenusw is equal to sum of square of other two sides

Answer 2

Answer:

Pythagorean triples are a^2+b^2 = c^2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).

The integer solutions to the Pythagorean Theorem, a2 + b2 = c2 are called Pythagorean Triples which contains three positive integers a, b, and c.

Example: (3, 4, 5)

By evaluating we get:

32 + 42 = 52

9+16 = 25

Hence, 3,4 and 5 are the Pythagorean triples.

You can say “triplets,” but “triples” are the favoured term. Let’s start this topic by an introduction of Pythagoras theorem.

Check if (7, 15, 17) are Pythagorean triples.

Solution:

(a, b, c) = (7, 15, 17)

We know that a2 + b2  = c2 

By substituting the values in the equation, we get

72 + 152 = 172

49 + 225 =  289

274 ≠ 289

Hence, the given set of integers does not satisfy the Pythagoras theorem, (7, 15, 17) is not a Pythagorean triplet. Also, it proves that the Pythagorean triples are not made up of all odd numbers.