Explanation:
it is not an equilateral triangle, because the 3 sides are not equally long.
it is not an isoceles triangle, because there is no pair of equally long sides.
so, it is a scalene triangle (3 different sides, 3 different angles).
it is not a right-angled triangle, because there is no combination of the side lengths 10, 12, 13 that can be arranged with the Pythagoras equality :
c² = a² + b²
10² (100), 12² (144) and 13² (169) cannot be arranged in any combination to achieve that equality.
it is not an obtuse triangle (with one angle being larger than 90°), because in an obtuse triangle the longest side is c and opposite of the large angle. so, in our case, 13 would have to be c. but the criteria for an obtuse triangle
a² + b² < c²
is not fulfilled (100 + 144 = 244, and that is larger than 169).
so, it is an acute triangle (all 3 angles are smaller than 90°).