Answer: The correct options are (A) Acute and (F) Scalene.
Step-by-step explanation: Given that the lengths of three sides of a triangle are 11.4 units, 9 units and 7 units.
We are to select all the correct classifications of the given triangle.
Since the lengths of all the three sides are different, so all the three sides are non-congruent.
So, the given triangle is a SCALENE triangle.
Also, we have
[tex](11.4)^2=129.96,\\\\9^2+7^2=81+49=130.[/tex]
So, we have
(11.4)² < 9² + 7².
That is, the square of the length of the largest side is less than the sum of the squares of the lengths of two smaller sides.
Therefore, the given triangle is an ACUTE-angled triangle.
Thus, the given triangle is ACUTE and Scalene.
Options (A) and (F) are correct.
