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.
A triangle with side lengths of 1 cm and 13 cm cannot exist. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to the Triangle Inequality Theorem. In this case, 1 + 13 = 14, which is not greater than 13. Therefore, a triangle with side lengths of 1 cm and 13 cm is not possible.
To classify a triangle by its sides, we look at the lengths of its sides. There are three main types of triangles based on side lengths: scalene, isosceles, and equilateral.
1. Scalene Triangle: In a scalene triangle, all three sides have different lengths. Since the given triangle has side lengths of 1 cm and 13 cm, which are different, and the length of the third side is unknown, we cannot classify it as scalene at this point.
2. Isosceles Triangle: In an isosceles triangle, two sides have the same length. Since the given triangle has side lengths of 1 cm and 13 cm, which are different, we cannot classify it as isosceles.
3. Equilateral Triangle: In an equilateral triangle, all three sides have the same length. Since the given triangle has side lengths of 1 cm and 13 cm, which are different, we cannot classify it as equilateral.
From the given information, we cannot determine the classification of the triangle by its sides.
To classify a triangle by its sides, we typically refer to it as either an equilateral, isosceles, or scalene triangle.
An equilateral triangle has all three sides of equal length.
An isosceles triangle has two sides of equal length.
A scalene triangle has all three sides of different lengths.
In this case, we are given that two sides of the triangle are 1 cm and 13 cm, respectively. We need to determine the length of the third side in order to classify the triangle.
To find the length of the third side, we need to apply the triangle inequality theorem. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to our triangle:
1 + 13 > x (where x represents the length of the third side)
14 > x
Since the lengths of the two known sides (1 cm and 13 cm) are greater than the length of the third side (x), we can conclude that any value of x that is smaller than 14 will satisfy the triangle inequality theorem.
Now, let's classify the triangle based on the lengths of its sides:
- If the length of the third side is less than 14, the triangle will be either isosceles or scalene.
- If the length of the third side is equal to 1 or 13, the triangle will be isosceles (two sides of equal length).
- If the length of the third side is different from 1 and 13, the triangle will be scalene (all sides of different lengths).
Note that we cannot have an equilateral triangle in this case since all three sides must be equal in length, and we are given that one side is 1 cm and another side is 13 cm.
Therefore, based on the information given, we can classify the triangle as either isosceles or scalene.