The lengths of two sides of right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? round your answer to the nearest tenth.

10.2 inches.

Step-by-step explanation:

First, assume the two sides are legs, square both sides and add them,:

144+225=369

square root of 369 is the hypotenuse

suppose 15 is the hypotenuse (it can't be 12 since the hypotenuse is the longest)

Then 12^2+x^2=15^2

x^2=81

x=9, a 9-12-15 right triangle.

So the third side can be 9 or square root of 369 = 19.2 to nearest tenth.

The difference is 19.2-9=10.2 inches.