The hypotenuse of a right triangle is 75 inches long. One leg is 5 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.
Solution:
Let the shortest side be x
Then the second side is x + 5
And the hypotenuse is 75 in. long.

Applying Pythagoras theorem,


i.e.  or Dividing it by 2 throughout

This can be solved using the quadratic solver as shown below.


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:
  
  
  
  For these solutions to exist, the discriminant  should not be a negative number.
  
  First, we need to compute the discriminant : .
  
  Discriminant d=11225 is greater than zero. That means that there are two solutions: .
  
    
    
    
    Quadratic expression  can be factored:
  
  Again, the answer is: 50.4740502510427, -55.4740502510427.
Here's your graph:




The solution is the positive value of x is 50.5 inches (rounded off), since the length of a side cannot be negative.

So the lengths of the sides are , , and  inches respectively.

:)