Answer: The given triangle is an obtuse triangle.
Step-by-step explanation: Let ABC be the given triangle, where the side lengths are as follows :
[tex]AB=87~\textup{cm},~~BC=21~\textup{cm},~\textup{and}~CA=93~\textup{cm}.[/tex]
We are to check whether ΔABC is acute, obtuse or right.
We know that ΔABC will be
(i) Acute, if AB² + BC² > CA²,
(ii) Obtuse, if AB² + BC² < CA²,
(iii) Right, if AB² + BC² = CA².
Now, we have
[tex]AB^2=87^2=7569,\\\\BC^2=21^2=441,\\\\CA^2=93^2=8649.[/tex]
So,
[tex]AB^2+BC^2=7569+441=8010<8649=CA^2.[/tex]
Therefore, the given triangle is an obtuse triangle.
