An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

Which best describes the range of possible values for the third side of the triangle?

x 18.9

12.5 < x < 18.9

x 26

6 < x < 26

- - Two sides of a triangle are 10cm and 16cm.

- - If the third side is less than 6cm, then it can't reach the open ends

of the 10cm and the 16cm, even if they're closed on top of each other ...

their ends are never less than 6cm apart.

- - If the third side is more than 26cm, then the 10cm and the 16cm

can't reach end-to-end of the 26cm, even if they're wide open and

in a straight line ... they can never span more than 26cm.

- - So the third line must be more than 6 cm and less than 26cm.

That's the last choice on the list: 6 < x < 26.

(I apologize in advance for any spelling errors, I'm typing on my phone D:)

There's a rule that says that any two sides of a triangle must add up to be greater than the third side.

We are given two side lengths, which means there are two possible cases:

1. 10 being the smallest side and 16 being the middle-length side.

2. 10 being the middle-length side and 16 being the longest side.

In case 1, the remaining side must be greater than 26 in order for 10+16 to be greater than the longest side.

In case 2, the remaining side must be at least 6 in order for 10 + the remaining side to be greater than 16.

Basically, the answer just needs to be greater than 6.

However, we are not looking for this exactly, because the question asks which range best describes it.

Answer 1: X could potentially be smaller than 6, so this answer must be incorrect.

Answer 2: X cannot be less than six here, so this answer is correct!

In answers 3 and 4, X could potentially be less than 6, so those answers are also incorrect.

Let me know if you have any questions : D