Sides of a Triangle Quick Check 4 of 54 of 5 Items 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 acute acute isosceles isosceles equilateral equilateral scalene scalene Skip to navigation page 15 of 15

Answer 1

To classify the triangle by its sides, we need to check the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

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

1. \( 1 + 13 > x \) → \( 14 > x \) (So \( x < 14 \))
2. \( 1 + x > 13 \) → \( x > 12 \)
3. \( 13 + x > 1 \) → \( x > -12 \) (This inequality is always satisfied for positive lengths.)

To satisfy both relevant inequalities \( x < 14 \) and \( x > 12 \), the only possible whole number value for \( x \) is 13 cm.

Thus we have the side lengths as 1 cm, 13 cm, and 13 cm.

Now to classify the triangle:

• Since two sides are equal (13 cm and 13 cm), the triangle is classified as isosceles.

So the correct response is isosceles.