Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side.
A. 4.5
B. 3.5
C. 4.2
D. 5.5
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. Therefore, to find a possible measure of the third side, we need to find the sum of the two given side lengths and then subtract it from the sum of those side lengths, which will give us the length of the third side.
Given: Side A = 3.7, Side B = 8.2.
To find the possible measure of the third side:
Third side = (Sum of Side A and Side B) - (Sum of Side A and Side B)
Third side = (3.7 + 8.2) - (3.7 + 8.2)
Third side = 11.9 - 11.9
Third side = 0
Since the length of the third side cannot be zero, D. 5.5 is not a possible measure for the third side.
Therefore, the possible measures of the third side are:
A. 4.5
B. 3.5
C. 4.2