How many pythagorean triples

Let us try generating a Pythagorean triple using the two integers 2 and 3. Since we know the values of m and n, it's time to substitute those values into the formulas of a, b, and c, to get the sides of the right triangle. Therefore, 5, 12, 13 are Pythagorean triples.

Example 1: John's mother asked him to place the ladder at such a distance from the wall, such that the 13 feet tall ladder's head falls exactly on the top of the 12 feet wall. Can you help John to find the distance of the ladder from the wall?

Solution: Let the required distance be 'x' feet. Here, the ladder, the wall, and the ground form a right-angled triangle. The ladder is the hypotenuse of the triangle. Example 2: Joey tried a new route to reach his school today. He walked 6 blocks to the north, and then 8 blocks to the west.

Can you find how far is his school from his home? Solution: The distance from the school to home is the length of the hypotenuse. Example 3: Check if 7, 12 and 19 are Pythagorean triples.

Also find, what could be the Pythagorean triples of 7? Thus we find 7, 12, 19 don't satisfy the equation. They are not Pythagorean Triples. To generate Pythagorean Triples, we check if the number is odd or even. Here 7 is odd. Pythagorean triples are the positive integers that fit the formula of the Pythagorean theorem. Example: 3,4,5 3, 4 and 5 share no common factors, so 3,4,5 is a primitive triple.

Example: 6,8,10 6, 8 and 10 share a common factor of 2, so 6,8,10 is not a primitive triple. But 6,8,10 is just 3,4,5 times 2. Pythagorean Triples - Basics Numbers Index. The 3,4,5 Triangle. Jakob Jakob 1. That said, this is a not very good answer to an old question that already has several good ones. This wastes your time and the time of those of us who track questions with new activity.

If you want to contribute, answer new questions. Please use mathjax to format mathematics: math. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post.

Linked Related 6.