An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s? 2 < s < 18 6 < s < 12.8 s 18 s 12.8

B. 6 < s < 12.8 is the answer

Here we need the "triangular inequality", which can be described as "The sum of the shorter sides of a triangle must be greater than the third side."

So if 8 and 10 cm are the shorter sides, then the third side must be smaller than 8+10=18 cm.

If the third side is the shortest, say s, then

s+8>10, in other words, s>2.

Therefore the third side must be between 2 and 18, or 2
Note that the inequalities are strict inequalities, that means the third side canNOT be equal to 2 or 18. This comes directly from the "triangular inequality" statement.