Question

State of triangle is acute, obtuse, or right?4)√108 mi5 miA) RightC) Acute9 miB) Obtuse

Answer 1

In order to find if the triangle is acute, right or obtuse, we need to compare the square of the bigger side (a) with the sum of squares of the other sides (b and c):

If a² > b² + c², the triangle is obtuse.

If a² = b² + c², the triangle is right.

If a² < b² + c², the triangle is acute.

So we have:

`\begin{gathered} a=√(108) \\ a^2=108\\ \\ b=9 \\ b^2=81\\ \\ c=5 \\ c^2=25\\ \\ b^2+c^2=81+25=106\\ \\ 108>106 \end{gathered}`

The triangle is obtuse, therefore the correct option is B.