Question

two sides of an obtuse triangle measure 12 inches and 14 inches .the longest side measures 14 inches .what is the greatedt possible whole number length of the unknown side?

Answer 1

The largest side of the triangle measures 14 in. The triangle is obtuse so no two sides can be of equal length.

The sides of the triangle must follows the following two rules:
a) The sum of any two sides must be greater than the third side.
b) The difference of any two sides must be greater than the third side. 

Since the largest side is 14, the unknown side will be smaller than 14. Only whole number values are allowed so the answer to this question will be 13.

For the side lengths 12, 13, 14, the sum of any two sides will be greater than the third side and difference of any two sides will be smaller than the two sides. The length is a whole number and the greatest positive number.

So, the greatest possible whole number length of the unknown side can be 13 inches.