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

Jun 25, 2015

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 ${41}^{2} = 1681$

Jun 27, 2015

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:

$a = 2 k + 3$

$b = \frac{{a}^{2} - 1}{2} = 2 {k}^{2} + 6 k + 4$

$c = \frac{{a}^{2} + 1}{2} = 2 {k}^{2} + 6 k + 5$

then it is a right angled triangle.

The first few examples are:

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