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 < 2 or s > 18 s < 6 or s > 12.8

Either the new side or 10 has to be the hypotenuse of a triangle.

Case one

The hypotenuse is 10
10^2 = 8^2 + b^2
b^2 = 36
b = 6 so the new side has to be more than 6 but less than 10.

Case two

The new side is the hypotenuse of a right triangle
8^2 + 10^2 = 64 + 100 = 164
sqrt(164) = 12.8
So the new side has to be less than 12.8 but greater than 6

Answer
The second one <<<<
6 < s < 12.8