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) which is the true correct response

Question

Responses

acute
acute

equilateral
equilateral

scalene
scalene

isosceles

Answer 1

To determine if a triangle with sides of lengths 1 cm and 13 cm can exist, we need to use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Here, we have:

1. Side 1: 1 cm
2. Side 2: 13 cm
3. Let the third side be \( x \).

According to triangle inequality:

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

From inequalities 1 and 2, we can see that:

• From \( x < 14 \) and \( x > 12 \), the only integer value for \( x \) is 13.

Now we have the side lengths as 1 cm, 13 cm, and 13 cm, which form a triangle.

Since this triangle has two equal sides (13 cm and 13 cm), it is classified as an isosceles triangle.

Thus, the correct response is isosceles.