Find which is a pythagorean triplet. * (5,13,12) (7,11,14) (5,7,5) (2,3,4)
Answers
Answer: look below
Step-by-step explanation:
Pythagorean triples are a2+b2 = c2 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). Learn Pythagoras theorem for more details.
Pythagoras who was a mathematician was interested in mathematics, science, and philosophy. He was born in Greece in about 570 BC. He is famous for a property of triangles with a right angle i.e 900 angles, and the property is known as Pythagoras Theorem. In a right-angled triangle, the hypotenuse is the side ‘r’, the side opposite the right angle. Adjacent to the right angle the shorter of the two sides is the side p. In this article, let us discuss what is Pythagorean triples, its formula, list, steps to find the triples, examples, and proof.
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.
Table
(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
(20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53)
(11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73)
(13, 84, 85) (36, 77, 85) (39, 80, 89) (65, 72, 97)
Pythagoras Triples Formula
If a triangle has one angle which is a right-angle (i.e. 90o), there exists a relationship between the three sides of the triangle.
If the longest side (called the hypotenuse) is r and the other two sides (next to the right angle) is called p and q, then:
p2 + q2 = r2.
or,
The sum of the squares of the other two sides is the same as the square of the longest side.
Step-by-step explanation:
To be Pythagorean triplets
Hypothenuse^2=Base^2+height^2
If(5,13,12)
Hypotenuse is 13
Base is 5
hight is 12
13^2=12^2+5^2
169=144+25
169=169
(5,13,12) is Pythagorean triplets