logo for solving-math-problems.com
leftimage for solving-math-problems.com

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

Click here to add your own comments

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



Feb 07, 2012
Pythagorean Triple
by: Staff


Part I

Question:

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:



Answer:

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:


A PYTHAGOREAN TRIPLE is simply a RIGHT TRIANGLE whose SIDES are positive INTEGERS.

An easy way to generate Pythagorean Triples is to multiply any known Pythagorean Triple by an integer (any integer).
Sides of a known triple: 3,4,5

Multiply by 2 = 6,8,10
….verification: 6² + 8² = 10² = 100
Multiply by 3 = 9,12,15
….verification: 9² + 12² = 15² = 225
Multiply by 4 = 12,16,20
….verification: 12² + 16² = 20² = 400
.
.
.

---------------------------------------------------

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com