Question

Is a triangle with sides of lengths 16, 30, and 35 a right triangle?

Answer 1

Using the Pythagorean Theorem to test if the sides result in a right triangle shows that they don't. So - no.

Explanation:

One way to explore this question is to apply a mathematical operation that we know only works for right triangles and see if it works for this set of lengths. The operation that comes to mind for me is the Pythagorean Theorem. So let's try it.

The Theorem states that for a right triangle,

`a^2+b^2=c^2`

where c is the hypotenuse and a and b are the two shorter sides.

So does our given lengths work? Let's see:

`16^2+30^2=35^2`

`256+900=1225`

`1156=1225`

`1156!=1225`

And as we can see, the two sides do not equal each other, so this means the sides do not make a right triangle.