Question

A triangle has side lengths 87cm 21cm and 93cm is the triangle acute obtuse or right

Answer 1

The triangle is obtuse.

Answer 2

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 :

$AB=87~\textup{cm},~~BC=21~\textup{cm},~\textup{and}~CA=93~\textup{cm}.$

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

$AB^2=87^2=7569,\\\\BC^2=21^2=441,\\\\CA^2=93^2=8649.$

So,

$AB^2+BC^2=7569+441=8010$

Therefore, the given triangle is an obtuse triangle.