# Questions tagged [pythagorean-triples]

Questions about Pythagorean triples, positive integer solutions to $a^2 + b^2 = c^2$.

390 questions
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### Is there a way of finding out the remaining two numbers of pythagorean triple if one of the side is given

I am solving one question related to right triangle and I have to find out the remaining two numbers of the pythagorean triple if one of the number is given. I know there can be many triples possible ,...
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### Pythagorean Triple where $a=b$?

I cannot find even a single webpage mentioning this topic. I'm a programmer and I'm looking for a 45-45-90 triangle where all of the sides are whole numbers. In the video I am watching, they say to ...
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### How to say that functions generate set members?

In a paper I am writing, I have seven abstract statements and, corresponding to the first one, I have a theorem statement that says I will prove that there is a Pythagorean triplet for every pair of ...
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### Pythagorean triples that “survive” Euler's totient function

Suppose you have three positive integers $a, b, c$ that form a Pythagorean triple: $$a^2 + b^2 = c^2. \tag{1}\label{1}$$ Additionally, suppose that when you apply Euler's ...
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### Matrix valued Pythagorean Triples

Consider any nxn matrices A, B and C such that A^2 + B^2 = C^2 Then the matrix triple (A,B,C) is called a Matrix valued Pythagorean Triple. I have observed that any nxn matrix M and N such that MN=NM,...
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### What is the area of the quadrilateral $ADEC$ in $ABC$ right triangle in the following diagram?

In the right angled triangle $ABC$, $\angle A = 90^\circ$, $AB=8$, $AC=6$, $BC = 10$. $D$ is a point on $AB$ in such way that if a perpendicular $DE$ is drawn on $BC$ from $D$ then $BE = 4$. What ...
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### Calculating length of triangle sides in trapezium

My younger brother has this mathematical problem to solve, and he came to me for help. At first I thought I could solve it by simply applying the Pythagorean theorem, but there seems to be more to it. ...
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### Can we find two non-congruent right triangles with whole-number lengths and congruent hypotenuses?

I know some ways to find some Pythagorean triples. And I understand that if $a^2 + b^2 = c^2$ then $(a-b)^2 + (a+b)^2 = 2c^2$. I feel like that suggests a way forward, but I cannot find that way. ...
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### Length of an edge

My sister asked me to help her with her homework for mathematics, however frustratingly I was not able to figure out how to solve it. The assignment is as follows where it was requested to calculate ...
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