Question

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
isosceles

acute
acute

scalene
scalene

equilateral

Answer 1

To determine the classification of the triangle based on its side lengths, we first need to ensure that it satisfies the triangle inequality theorem:

For any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must hold:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

In your case, we have two sides measured as 1 cm and 13 cm. Let's denote the third side as \( x \).

Now, we will apply the triangle inequality conditions:

1. \( 1 + 13 > x \)
\( 14 > x \)
Thus, \( x < 14 \).

2. \( 1 + x > 13 \)
\( x > 12 \).

3. \( 13 + x > 1 \)
This condition is always satisfied for positive \( x \).

From the inequalities \( x < 14 \) and \( x > 12 \), we find that the only possible integer value for \( x \) is \( 13 \).

Thus, the side lengths of the triangle are 1 cm, 13 cm, and 13 cm.

Now let's classify the triangle by its sides:

- It has two sides of equal length (13 cm), making it an **isosceles triangle**.

Therefore, the answer is **isosceles**.