Determine the length of the third side of a triangle from the choices provided if the first two sides measured 10 and 12

Answer 1

To find the length of the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the first two sides of the triangle measure 10 and 12, the sum of these two sides is 10 + 12 = 22.

Now, let's consider the options provided:

A) 19
B) 21
C) 23
D) 24

Using the triangle inequality theorem, we can eliminate option A (19) as the sum of the first two sides (10 + 12 = 22) is already greater than 19.

For option B (21), the sum of the first two sides (10 + 12 = 22) is greater than 21, so this could be a possible length for the third side.

For option C (23), the sum of the first two sides (10 + 12 = 22) is not greater than 23, so this is not a valid length for the third side.

For option D (24), the sum of the first two sides (10 + 12 = 22) is not greater than 24, so this is also not a valid length for the third side.

Therefore, the possible length for the third side of the triangle is 21, so the correct answer is B) 21.