SOLUTION: The lengths of two sides of a 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 answ

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Question 1037473: The lengths of two sides of a 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.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The sum of the lengths of two sides must be greater than the third side.
To the nearest tenth, the third side could be 3.1 inches, which is just enough to make a triangle with 12 inches and 15 inches. 12+3.1>15,1
Alternatively, it could be 26.9 inches, were the other two lengths nearly a straight line. 12+15>26.9
The answer to the question is not 23.8 inches, the difference between the two, but 23.9 inches, because anything slightly greater than 3 inches or slightly less than 27 inches would work, and rounding it higher would be a tautology. A case may be made for either length.
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
The lengths of two sides of a 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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  One possibility is 12 inches is the leg, 15 inches is the hypotenuse.
    Then the third side (which is the second leg in this case) is 
    
     =  = 9 in
    
    (of course, it is 3:4:5 right-angled triangle).

2.  Another possibility is that both sides of 12 in and 15 in are the legs.
    Then the hypotenuse is 
    
     =  = 19.21 in (approximately).


The difference between 19.21 in and 9 in is 

    19.21 - 9 = 10.21 in.


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