Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point) Responses 22 22 30 30 24 24 15
To determine the length of the third side of a triangle, we can apply 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.
In this case, let's check the sum of the lengths of the first two sides (10 and 12) with each answer choice:
22: 10 + 12 = 22 (valid)
30: 10 + 12 = 22 (not valid)
24: 10 + 12 = 22 (valid)
15: 10 + 12 = 22 (not valid)
Based on the triangle inequality theorem, the only valid response is 22.