Question

Can the sides 9, 40, 41 be a right triangle?

Answer 1

Yes. These can be the lenghts of a right triangle sides

Explanation:

To solve such task you can use the inverse Pytagorean Theorem. You have to check if the square of the largest number equals the sum of squares of the other numbers.

In this case you have to check if `9^2+40^2=41^2`, which is true because `81+1600=1681` and `41^2=1681`

Answer 2

Yes, a 9,40,41 triangle is right angled since `9^2+40^2 = 41^2`.

This triangle is in the same sequence of right angled triangles whose first member is the 3,4,5 triangle.

Explanation:

If a triangle has sides:

`a = 2k+3`

`b = (a^2-1)/2 = 2k^2+6k+4`

`c = (a^2+1)/2 = 2k^2+6k+5`

then it is a right angled triangle.

The first few examples are:

`3,4,5`
`5,12,13`
`7,24,25`
`9,40,41`