Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 2 feet and 40 inches.

Answer 1

40 inches = 3 feet 4 inches = 3 and 1/3 feet.

X is the length of the 3rd side.....

The sum of any two sides must be (Strictly) greater than the third...

1st:

X+(3 and 1/3) > 2 ----> X > -1 and 1/3

this does not tell us very much; distance must be positive anyway

2nd:

X + 2 > 3 and 1/3

X > 3 and 1/3 - 2 = 1 and 1/3 <--- this is helpful

3rd:

3 and 1/3 + 2 > x

5 and 1/3 > x <---- this is helpful

combining the two helpful inequalities

1 and 1/3 < x < 5 and 1/3

So the missing side MUST be between 1 and 1/3 and 5 and 1/3