In Geometry Tutoring we know that a natural number, n , is said to be the perfect square of the natural number, a, if n = a*a . In other words, we can say that a natural number is called a perfect square if it is the square of some other natural number. By the term square of a number, we mean that the product of a number multiplied by itself.
Then we have also learnt some properties of perfect squares. Adding to such list of properties, we will learn one important property of perfect squares here. This property of perfect squares is called the Pythagorean triples. Let’s define the term first.
Three natural numbers m, n, p are said to to form a Pythagorean triples if m Ì‚2 + n Ì‚2 = p Ì‚2
The Pythagorean triples formula comes from the Phythagorean Theorem of right triangles in which the square of the length of hypotenuse is equal to the sum of the squares of the other two sides. In Pythagoras theorem, given a, b to be the two sides of a right triangle & h as the hypotenuse of the triangle, we have the relation h Ì‚2 = a Ì‚2 + b Ì‚2. According to Pythagorean triples formula , if m is a natural number greater than 1 , i.e., m>1, we can find a Pythagorean triples using the formula ,
( 2m , m Ì‚2 – 1 , m Ì‚2 +1 )
Lets take an example from Andhra Pradesh Board sample papers
Putting m = 4 , we get the Pythagorean triples as
2m = 2 * 4 = 8
m Ì‚2 – 1 = 16 – 1 = 15
m Ì‚2 + 1 = 16 + 1 = 17
Thus , the numbers 8, 15, 17 form the Pythagorean triples. For more information read here
This was all about Pythagorean triples. Visit our blogs for more information on Perpendicular Linesplanes and pythagorean theorem in grade vii
Then we have also learnt some properties of perfect squares. Adding to such list of properties, we will learn one important property of perfect squares here. This property of perfect squares is called the Pythagorean triples. Let’s define the term first.
Three natural numbers m, n, p are said to to form a Pythagorean triples if m Ì‚2 + n Ì‚2 = p Ì‚2
The Pythagorean triples formula comes from the Phythagorean Theorem of right triangles in which the square of the length of hypotenuse is equal to the sum of the squares of the other two sides. In Pythagoras theorem, given a, b to be the two sides of a right triangle & h as the hypotenuse of the triangle, we have the relation h Ì‚2 = a Ì‚2 + b Ì‚2. According to Pythagorean triples formula , if m is a natural number greater than 1 , i.e., m>1, we can find a Pythagorean triples using the formula ,
( 2m , m Ì‚2 – 1 , m Ì‚2 +1 )
Lets take an example from Andhra Pradesh Board sample papers
Putting m = 4 , we get the Pythagorean triples as
2m = 2 * 4 = 8
m Ì‚2 – 1 = 16 – 1 = 15
m Ì‚2 + 1 = 16 + 1 = 17
Thus , the numbers 8, 15, 17 form the Pythagorean triples. For more information read here
This was all about Pythagorean triples. Visit our blogs for more information on Perpendicular Linesplanes and pythagorean theorem in grade vii
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