If two sides of a triangle are 3 cm and 5 cm in length, which could NOT be the measure of the third side?

A) 2 cm

B) 3 cm

C) 4 cm

D) 5 cm

I thhink it's A

The sum of any two sides has to be greater than the third side

If third side is 2 from A
then 2+3 is not greater than 5

so A

To determine which could NOT be the measure of the third side of the triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.

Let's apply this to the given question. The two sides of the triangle are 3 cm and 5 cm in length.

For option A) 2 cm:
To determine if it could be the third side, we add the given two sides and compare the sum to the third side: 3 cm + 5 cm = 8 cm. Since 8 cm is greater than the length of the third side (2 cm), option A) could be the measure of the third side. So, it's not the correct answer.

For option B) 3 cm:
Again, we add the given two sides: 3 cm + 5 cm = 8 cm. Since 8 cm is greater than the length of the third side (3 cm), option B) could also be the measure of the third side.

For option C) 4 cm:
Once again, we add the given two sides: 3 cm + 5 cm = 8 cm. Since 8 cm is greater than the length of the third side (4 cm), option C) could be the measure of the third side.

For option D) 5 cm:
Adding the given two sides: 3 cm + 5 cm = 8 cm. This time, the sum of 8 cm is equal to the length of the third side (5 cm). 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, not equal to it. Therefore, option D) could NOT be the measure of the third side.

So, your answer is correct. The length of the third side of the triangle cannot be 5 cm.

To determine which measurement could not be the measure of the third side of the triangle, we need to refer to the triangle inequality theorem. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for each option:

A) 2 cm:

If we have sides of 3 cm and 5 cm, the sum of their lengths is 3 cm + 5 cm = 8 cm. However, 2 cm is less than 8 cm, so it is not a valid measure for the third side.

B) 3 cm:

The sum of the lengths of the given sides is 3 cm + 5 cm = 8 cm. In this case, 3 cm is equal to 8 cm, so it satisfies the triangle inequality theorem.

C) 4 cm:

The sum of the lengths of the given sides is 3 cm + 5 cm = 8 cm. In this case, 4 cm is less than 8 cm, so it satisfies the triangle inequality theorem.

D) 5 cm:

The sum of the lengths of the given sides is 3 cm + 5 cm = 8 cm. In this case, 5 cm is equal to 8 cm, so it satisfies the triangle inequality theorem.

Therefore, the measure that cannot be the length of the third side is A) 2 cm.