Question

What type of triangle has side lengths 2, √11, and √15?A. not a triangleB. acuteC. rightD. obtuse

Answer 1

We havae a triangle with the next measures:

- a = 2

- b = √11

- c = √15

To know if the triangle is acute, right or obtuse we must use the next statement

Now, we must calculate

`a^2+b^2`

And then we must compare it with

`c^2`

So,

`\begin{gathered} a^2+b^2 \\ =2^2+(\sqrt[]{11})^2 \\ =4+11 \\ =15 \end{gathered}`

And

`\begin{gathered} c^2 \\ =(\sqrt[]{15})^2 \\ =15 \end{gathered}`

Finally, we can see that

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

So, it is a right triangle.