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 equilateral equilateral scalene scalene isosceles isosceles acute acute Skip to navigation

Answer 1

To determine the type of triangle that can be formed with side lengths of 1 cm and 13 cm, we first need to find a possible length for the third side.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we can set up the following inequalities using the known sides (1 cm and 13 cm) and let \( c \) be the length of the third side:

1. \( 1 + 13 > c \) → \( c < 14 \)
2. \( 1 + c > 13 \) → \( c > 12 \)
3. \( 13 + c > 1 \) → \( c > -12 \) (this inequality is always true for positive lengths)

From the first two inequalities, we have:

• \( c < 14 \)
• \( c > 12 \)

This means that the only possible value for \( c \) that is a whole number is \( c = 13 \).

Now we have the side lengths: 1 cm, 13 cm, and 13 cm.

Since two sides are equal (1 cm and 13 cm), the triangle can be classified as isosceles.

Thus, the final classification of the triangle by its sides is isosceles.