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)%0D%0AResponses%0D%0A%0D%0Aequilateral%0D%0Aequilateral%0D%0A%0D%0A acute%0D%0A acute%0D%0A%0D%0Aisosceles%0D%0Aisosceles%0D%0A%0D%0Ascalene

Answer 1

To classify the triangle by its sides when two side lengths are given as 1 cm and 13 cm, we first need to determine the length of the third side.

According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's denote the sides as:

• Side A = 1 cm
• Side B = 13 cm
• Side C = x cm (the length of the third side, which is unknown).

From the triangle inequality, we have:

1. \(A + B > C\) → \(1 + 13 > x\) → \(x < 14\)
2. \(A + C > B\) → \(1 + x > 13\) → \(x > 12\)
3. \(B + C > A\) → \(13 + x > 1\) (This condition is always satisfied since x is positive.)

From conditions 1 and 2, we can conclude:

• \(12 < x < 14\)

The only integer value for x that satisfies this inequality is \(x = 13\).

So, the three sides of the triangle are:

• 1 cm
• 13 cm
• 13 cm

Now we classify the triangle:

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

Therefore, the answer is isosceles.