Question

The hypotenuse of a right-triangle is 52 units and all its sides have integer lengths. Then the perimeter of the triangle is ________ units

Answer 1

$\huge\red{A}\pink{N}\orange{S}\green{W}\blue{E}\gray{R}$

CORRECT ANSWER ➡️ 2367 °

Answer 2

ANSWER ⋇⋆✦⋆⋇　

Right-angled triangles with whole number sides have fascinated mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, can be seen a list of such triangles. So what is so fascinating about them? This page starts from scratch and has lots of facts and figures with several online calculators to help with your own investigations.

Contents of this page

The Things To Do icon means there is a Things to do section of questions to start your own investigations. The calculator calculator icon indicates that there is a live interactive calculator in that section.

1 Right-angled Triangles and Pythagoras' Theorem

1.1 Pythagoras and Pythagoras' Theorem

1.2 Some visual proofs of Pythagoras' Theorem

1.3 The 3-4-5 Triangle

1.4 Test a Triangle - is it Pythagorean?

1.4.1 PT?: Is it Pythagorean? Calculator

1.5 More Pythagorean Triples

1.6 Graphs of the numbers of Pythagorean Triangles

2 Methods of Generating Pythagorean Triangles

2.1 The simplest method of finding all Pythagorean triples

2.2 A simple two-unit-fraction method of generating PTs

2.2.1 Two consecutive odd unit fractions

2.2.2 Two consecutive even unit fractions

2.3 The Two-Fractions method of generating Pythagorean Triples

2.3.1 Generate PTs using Two Fractions Calculator

2.3.2/ You Do The Maths...

2.4 The m,n formula for generating Pythagorean Triples

2.4.1 Are all the Pythagorean triples generated by m,n?

2.4.2 Generate PTs using the m,n formula Calculator

2.4.3 The two-fraction method and the m,n generators method

2.5 The Fibonacci method

2.5.1 PTs from a Fibonacci sequence Calculator

2.5.2 The Fibonacci method and the m,n formula method

2.6 Hypotenuse-Leg difference

2.7 An easy method of writing down a series of Triples

3 Patterns in Pythagorean Triples

3.1 Hypotenuse and Longest side are consecutive

3.2 The two legs are consecutive

3.2.1 The m,n values for consecutive-legs triangles

3.2.2/ You Do The Maths...

3.3 Another Side Difference - the excess

3.4 More patterns

4 Can any number be a side in some Pythagorean Triangle?

4.1 The Number of Pythagorean Triangles having a side n

4.2 The Possible Sides of Pythagorean Triangles

4.3 Number Series in Pythagorean Triangles

4.4 Graphs of the Primitive Triples

4.4.1 Plotting all Pythagorean Triangles

4.4.2 Plotting the Primitive Pythagorean triangles

5 The UAD Tree of Primitive Pythagorean