Question

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown.

Answer 1

The longest side of a triangle is known as the hypotenuse. To find the hypotenuse you would use the equation a^2+b^2=c^2
The a and b represent one side of the triangle so it wouldn't matter which side you use for them. The c represents the hypotenuse.
When you plug in the side lengths the equation would be: 10^2+15^2=c^2
100+225=c^2
325=c^2
Now you find the square root of 325 which is approximately 18
Final answer is 18 inches.

Answer 2

Having 2 triangle sides is not enough information. You'd also need at least one angle.
Anyway, when 2 sides are known the third side must be greater than the DIFFERENCE of the other side two sides and must be less than the SUM of the other 2 sides.
So third side must be greater than 5 (15 minus10) and must be less than 25 (10 plus 15)