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)
choose one.

isosceles

scalene

equilateral

acute

Answer 1

To classify the triangle by its sides, we must confirm that the given side lengths can indeed form a valid triangle. The side lengths given are 1 cm and 13 cm. Let's denote the third side as \( x \).

For a valid triangle, the triangle inequality must hold true, which states:

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

For the side lengths \( a = 1 \) cm, \( b = 13 \) cm, and \( c = x \):

1. \( 1 + 13 > x \) → \( 14 > x \) (which means \( x < 14 \))
2. \( 1 + x > 13 \) → \( x > 12 \)
3. \( 13 + x > 1 \) (this condition will always be true since \( x > 0 \))

From these inequalities, we can combine the first two conditions:

- From \( x < 14 \) and \( x > 12 \), we see that the only integer value satisfying this is \( x = 13 \).

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

Now, to classify the triangle:

- Since two sides are equal (13 cm and 13 cm), it is an **isosceles triangle**.

So the answer is **isosceles**.