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 greatest whole number length for the unknown side of an obtuse triangle with the other two sides measuring 12 and 14 inches is 13 inches, as per the triangle inequality theorem.

Step-by-step explanation:

To determine the greatest possible whole number length of the unknown side of an obtuse triangle with the other two sides measuring 12 inches and 14 inches, with 14 inches being the longest side, we can use the properties of triangles. The longest side, in this case, must be opposite the obtuse angle. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, to find the greatest possible length of the unknown side which we will call 'x', the inequality we must consider is:

12 + x > 14

Solving this inequality, we get:

x > 2

Since x must be an integer, the greatest possible whole number length for x would be the largest integer less than 14, because 14 plus any integer greater is never less than 14. So, the greatest possible whole number length of the unknown side is:

x = 13 inches

Answer 2

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.