Pythagorean triplets

Geometry Level 3

Read the following statements

1) $n, n+1$ are two consecutive positive integers. A Pythagorean triplet can be formed, if $n$ and $n+1$ are the two sides of the Right angled triangle(excluding hypotenuse).
2) $n, n+10$ are two integers( $n$ being a positive integer).A Pythagorean triplet can be formed, if $n$ and $n+10$ are the two sides of the Right angled triangle(excluding hypotenuse).
3) $n, n+30$ are two positive integers( $n$ being a positive integer). A Pythagorean triplet can be formed, if $n$ and $n+30$ are the two sides of the Right angled triangle(excluding hypotenuse).

Which of the above statements are true?

Clarification: A Pythagorean triplet is a set of three integers which satisfy the pythagorean theorem .

first statement is correct first and third statement is correct. first and second statement is correct All the three are true second and third statement is correct.

1 solution

Abhay Tiwari
Apr 28, 2016

The statements can be verified by checking only one Pythagorean triplet, which is $(3, 4, 5)$ .

Now, from this set of triplet, many other triplets can be derived, like we have $(3\times2=6, 4\times2=8, 5\times2=10$ .

Similarly, $(3\times10=30), (4\times10=40), and, (5\times10=50)$ and can be done for the third statement similarly by multiplying each number of the triplet $(3, 4, 5)$ by $30$ .

Clik here for more information on Pythagorean triplets.

The problem is defective as let n equal 4, thus the two numbers are 4 and 5, which cannot be used to determine the length of an integer hypotenuse.

Elijah L - 2 years, 9 months ago

Pythagorean triplets

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