Answer:
The correct options for the possible lengths of the third side are;
13 inches
28 inches
Step-by-step explanation:
The given lengths of two sides of the triangle are;
The length of one side of the triangle = 1 foot = 12 inches
The length of the other side of the triangle = 20 inches
The question can be solved by the triangle inequality theorem as follows;
A + B > C
B + C > A
A + C > B
Let the given sides be A = 12 inches and B = 20 inches
We have;
12 + 20 = 32 > C
Therefore, by the triangle inequality theorem, the third side, 'C', is less than 32 inches
Similarly, when C = 6 inches, we have;
A + C = 12 + 6 = 18 < B = 20
Therefore, the third side cannot be 6 inches
when C = 13 inches, we have;
A + C = 12 + 13 = 25 > B = 20
Therefore, the third side can be 13 inches
when C = 28 inches, we have;
A + C = 12 + 28 = 30 > B = 20
Therefore, the third side can be 28 inches
