  # Math 126 - Pythagorean Triple

by Angel
(VA)

Intro Paragraph:

Pythagorean Triple #1:

Build/generate a triple using one of many formulas available online. Please show your work. Note – please remember that using the Pythagorean formula ONLY does NOT constitute building or generating the triples. You must build/generate them using a different formula (such as the one above) and then CHECK to make sure that they form a triple by using the Pythagorean theorem, a^2+b^2 = c^2.

• The Triple is:

Check your work using the Pythagorean Theorem equation here.

Pythagorean Triple #2:

*Build/generate a triple using one of many formulas available online. Please show your work.

• The Triple is:

Check your work using the Pythagorean Theorem equation here.

Pythagorean Triple #3:

Build/generate a triple using one of many formulas available online. Please show your work.

• The Triple is:

Check your work using the Pythagorean Theorem equation here.

Pythagorean Triple #4:

Build/generate a triple using one of many formulas available online. Please show your work.

• The Triple is:

Check your work using the Pythagorean Theorem equation here.

Pythagorean Triple #5:

Build/generate a triple using one of many formulas available online. Please show your work.

• The Triple is:

Check your work using the Pythagorean Theorem equation here.

Conclusion Paragraph:

### Comments for Math 126 - Pythagorean Triple

 Feb 07, 2012 Pythagorean Triple by: Staff --------------------------------------------------- Part II Sides of a known triple: 5,12,13 Multiply by 2 = 10,24,26 ….verification: 10² + 24² = 26² = 676 Multiply by 3 = 15,36,39 ….verification: 15² + 36² = 39² = 1521 Multiply by 4 = 20,48,52 ….verification: 20² + 48² = 52² = 2704 . . . Sides of a known triple: 7,24,25 Multiply by 2 = 14,48,50 ….verification: 14² + 48² = 50² = 2500 Multiply by 3 = 21,72,75 ….verification: 21² + 72² = 75² = 5625 Multiply by 4 = 28,96,100 ….verification: 28² + 96² = 100² = 10000 . . . *Build/generate a triple using one of many formulas available online. Please show your work. There are many formulas A Pythagorean Triple (a² + b² = c²) can be calculated using the following method: Choose ANY TWO INTEGERS: x and y. y must be greater than x. The sides of a new Pythagorean Triple are: a = 2*x*y, b = y² - x², and c = y² + x² for example, let x = 5 and y = 6 a = 2*x*y = 2*5*6 = 60 b = y² - x² = 6² - 5² = 36 – 25 = 11 c = y² + x² = 6² + 5² = 36 + 25 = 61 the sides of the new Pythagorean Triple are: 60,11,61 ….verification: 60² + 11² = 61² = 3721 The formula shown in the last example will not give all possible Pythagorean Triples. To calculate all possible Pythagorean Triples, use the following formula: a = 2*d*x*y b = d*(y^2 - x^2) c = d*(y^2 + x^2) d = any positive integer y > x > 0 x and y must be positive integers x and y must be even, odd; or odd, even integers Thanks for writing. Staff www.solving-math-problems.com