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How can you tell if three positive numbers form a Pythagorean triple?
Wiki User
∙ 10y ago
The Pythagorean thereom is a^2+b^2=c^2. So, you can tell if they are a Pythagorean triple by seeing if the two smaller numbers squared equal the largest number squared. Example. Are 3,4, and 5 a Pythagorean triple? 3^2= 9. 4^2= 16. 5^2= 25. 9+16=25, so they are a triple.
Wiki User
∙ 10y ago
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What is a pythagorean triple?
A Pythagorean triple is three positive integers a, b, and c, such that a^2 + b^2 = c^2. A well known Pythagorean triplet is (3,4,5). If (a, b, c) is a Pythagorean triplet, then so is (ka, kb, kc) for any positive integer k.
How could you determine if a set of three numbers defines a right triangle?
If they are a Pythagorean triple then they will form a right angle triangle
What are Pythagorean Triples?
A Pythagorean Triple is a set of three numbers that are related like this:(The square of one of them) = (the square of another one) + ( the square of the third one)If three numbers are related that way, then they can be the lengths of the sides ofa right triangle. If they're not, then they can't.They're called a "Pythagorean Triple" because the ancient Greek mathematician Pythagoraswas the one who wrote the famous formula that describes the relationship among thesides of every right triangle. That's his formula, up in the second line of this answer.
Can a pythagorean triple have two equal sides?
In any Pythagorean triple, the square of the two shortest sides is equal to the square of the longest side. For example, 32+42=52. Since it is impossible to have a right-angled triangle with a side of 1, it is impossible for two sides of a right-angled triangle to be of the same length.Therefore, a Pythagorean triple will always contain three differently-sized sides.
Do these three sides make a sides make a right triangle 6 10 and 8?
Indeed they do, it is a Pythagorean Triple: 6*6 + 8*8 = 10*10. (62 + 82 = 102, 36 + 68 = 100, 100 = 100) The "basic" Pythagorean Triple of a 3, 4, 5 triangle works out like this: 32 + 42 = 52 9 + 16 = 25 25 = 25 Your triangle, the 6, 8, 10, figure, is a "doubling" of the cited "basic" triple, and any multiple of a Pythagorean Triple will also be another Pythagorean Triple, and a right triangle.
What is a pythagorean triple?
A Pythagorean triple is three positive integers a, b, and c, such that a^2 + b^2 = c^2. A well known Pythagorean triplet is (3,4,5). If (a, b, c) is a Pythagorean triplet, then so is (ka, kb, kc) for any positive integer k.
What is the name given to three whole numbers that can be the three sides of a right angled triangle?
Pythagorean triple
How could you determine if a set of three numbers defines a right triangle?
If they are a Pythagorean triple then they will form a right angle triangle
What are Pythagorean Triples?
A Pythagorean Triple is a set of three numbers that are related like this:(The square of one of them) = (the square of another one) + ( the square of the third one)If three numbers are related that way, then they can be the lengths of the sides ofa right triangle. If they're not, then they can't.They're called a "Pythagorean Triple" because the ancient Greek mathematician Pythagoraswas the one who wrote the famous formula that describes the relationship among thesides of every right triangle. That's his formula, up in the second line of this answer.
Can a Pythagorean triple begin with any even number?
Yes. Select any triple and if the first one is not even, then double all three numbers. For example, (3, 4, 5) gives (6, 8, 10).
WHAT is three dimensional and infinitely large?
The set of Pythagorean triple is three dimensional and infinitely large.
A flowchart to Accept three numbers and check whether it firms to Pythagorean triplet?
Accept 3 natural numbers and check whether it firms pythagorean triplet
Can a pythagorean triple have two equal sides?
In any Pythagorean triple, the square of the two shortest sides is equal to the square of the longest side. For example, 32+42=52. Since it is impossible to have a right-angled triangle with a side of 1, it is impossible for two sides of a right-angled triangle to be of the same length.Therefore, a Pythagorean triple will always contain three differently-sized sides.
Do these three sides make a sides make a right triangle 6 10 and 8?
Indeed they do, it is a Pythagorean Triple: 6*6 + 8*8 = 10*10. (62 + 82 = 102, 36 + 68 = 100, 100 = 100) The "basic" Pythagorean Triple of a 3, 4, 5 triangle works out like this: 32 + 42 = 52 9 + 16 = 25 25 = 25 Your triangle, the 6, 8, 10, figure, is a "doubling" of the cited "basic" triple, and any multiple of a Pythagorean Triple will also be another Pythagorean Triple, and a right triangle.
Is there a rule that helps you figure out how many odd numbers can make up a Pythagorean triple?
Yes. The square of an odd number is odd. So, if a, b and c are odd then a2, b2 and c2 are also all odd. But the sum of two odd numbers must be even. So for these to be Pythagorean, all three squares cannot be odd. Thus there are no odd triplets.
How does Euclid's Formula Work?
Euclid's Formula is a method of generating Pythagorean Triples. A Pythagorean Triple is a set of three positive integers (whole numbers), which satisfy the equation a2 + b2 = c2. The smallest Pythagorean Triple is 3, 4, 5. Euclid's Formula says this: If you choose two positive integers m and n, with m < n, then the three numbers n2 - m2, 2mn and n2 + m2 form a Pythagorean Triple. For example, if m = 5 and n = 7, n2 - m2 = 49 - 25 = 24, 2mn = 70, and n2 + m2 = 49 + 25 = 74. 24, 70, 74 is a PT, because 242 + 702 = 742. That's how to use Euclid's Formula. If the question means why does it work, then: (n2 - m2)2 + (2mn)2 = (n4 + m4 - 2n2m2) + (4m2n2) = n4 + m4 + 2n2m2, which is the same thing as (n2 + m2)2 . Two things to note are: The Formula does not generate all possible Triples, and it will generate Primitive Triples (ones with no common factor), only if m and n have no common factor, (except 1).
What is the sign of the product of three integers with the same sign?
The product of three positive numbers is positive. The product of three negative numbers is negative.
