two sides of a triangle have lengths of 8 inches and 12 inches. which could be the length of the third side

A. 2 in
B. 4 in
C. 16 in.
D. 20 in
i think C? or D?

Is this a right triangle?

To determine which option could be the length of the third side of the triangle, we can use the Triangle Inequality Theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's apply this theorem to the given lengths of the two sides:

8 inches + 12 inches = 20 inches.

Therefore, any potential length for the third side must be greater than 20 inches. Let's analyze the options:

A. 2 inches: Since 8 + 2 = 10 inches, this option does not satisfy the theorem. The sum of the two given side lengths is greater than the third side, so option A cannot be the length of the third side.

B. 4 inches: Since 8 + 4 = 12 inches, this option does not satisfy the theorem either. Again, the sum of the two given side lengths is equal to the third side, so option B cannot be the length of the third side.

C. 16 inches: Since 8 + 16 = 24 inches, this option satisfies the theorem. The sum of the two given side lengths is greater than the third side, so option C could be the length of the third side.

D. 20 inches: Since 8 + 20 = 28 inches, this option also satisfies the theorem. The sum of the two given side lengths is greater than the third side, so option D could be the length of the third side as well.

In conclusion, options C (16 inches) and D (20 inches) could both be the possible length of the third side.