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

the greates possible whole-number length of the unknown side is 7 inches

Explanation:

1) An obtuse triangle has an angle greater than 90°.

2) The longest side of an obtuse triangle is the side opposed to the greatest angle (the angle greater tha 90°).

3) If the longest side measures 14 in and the other known side measures 12 in, the upper bound of the other side is when the triangle is a right triangle whose hypotenuse is the longest side: 14 in.

4) Therefore there is an upper bound to the other side when you have a righ triangle and you can use Pytagorean theorem:

14^2 = 12^2 + x^2

=> x^2 = 14^2 - 12^2 = 196 - 144 = 52

=> x = √52

=> x = 7.2

That means that the greatest value of x is below 7.2 in, which in whole- numbers is 7 in, which is the greatest whole-number length of the unknown side.

Hi,

The largest possible number is 7 inches.

Hope this helps!