A triangle’s side lengths are whole numbers. If the measure of two of its sides are 1 cm and 13 cm, classify the triangle by its sides.(1 point)
Responses
isosceles
scalene
equilateral
acute
scalene
To classify the triangle by its sides, we need to consider the lengths of all three sides.
Given that two sides of the triangle measure 1 cm and 13 cm, we can determine the possible lengths for the third side by applying the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Since the two known side lengths are 1 cm and 13 cm, the possible range of the third side length is from 13 - 1 = 12 cm to 13 + 1 = 14 cm.
Now we can analyze the different possibilities:
1. If the third side has a length of 12 cm, then the triangle would have side lengths of 1 cm, 12 cm, and 13 cm. In this case, the triangle would be classified as an isosceles triangle because two sides (1 cm and 13 cm) are equal.
2. If the third side has a length of 14 cm, then the triangle would have side lengths of 1 cm, 13 cm, and 14 cm. In this case, the triangle would be classified as a scalene triangle because all three sides have different lengths.
Since the problem does not specify a specific third side length, we have two possible classifications for the triangle based on its sides: isosceles and scalene.