What is the rule for Pythagorean triples?

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Do Pythagorean triples have to be whole numbers?

See, Pythagorean triples are the integers that fit the formula for the Pythagorean Theorem. These are whole numbers that can’t be decimals. Because all Pythagorean triples solve the formula for the Pythagorean Theorem, you can take any Pythagorean triple and make a right triangle out of it.

Can a Pythagorean triple have all odd numbers?

A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number because according to the properties of a square number, the square of an odd number is an odd number and the square of an even number is an even number.

How do you find the hypotenuse in Pythagorean triples?

Pythagorean theorem The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the two sides. This is usually expressed as a2 + b2 = c2. Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are (3,4,5) and (5,12,13).

Can the hypotenuse be a decimal?

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle. The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: \displaystyle \sqrt{289}=17.

Why are Pythagorean triples endless?

But 2 n +1 comprises all the odd numbers; every other square numbers is odd; there are an infinite number of odd squares; hence there are an infinite number of Pythagorean triples. …

What is the hypotenuse in Pythagorean?

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

Why does the hypotenuse leg theorem work?

According to the hypotenuse leg theorem, if the hypotenuse and one leg of one right triangle are congruent to the other right triangle’s hypotenuse and leg side, then the two triangles are congruent. The hypotenuse leg theorem is a criterion that is used to prove the congruence of triangles. …