Question

Can the sides 30, 40, 50 be a right triangle?

Answer 1

If a right angled triangle has legs of length `30` and `40` then its hypotenuse will be of length `sqrt(30^2+40^2) = 50`.

Explanation:

Pythagoras's Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

`30^2+40^2 = 900+1600 = 2500 = 50^2`

Actually a `30`, `40`, `50` triangle is just a scaled up `3`, `4`, `5` triangle, which is a well known right angled triangle.

Answer 2

Yes it can.

Explanation:

To find out whether the triangle with sides 30, 40, 50, you would need to use the Pythagoras theorem `a^2+b^2=c^2` (equation for calculating unknown side of a triangle).
Substituting the variables we get the equation `30^2+40^2=c^2` we won't substitute 50. because we are trying to find whether this equals 50
`30^2+40^2=c^2`
`2500=c^2`
`sqrt2500=c`
`50=c`
Therefore because 'c' equals 50 we know that this triangle is a right triangle.