SOLUTION: 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 t

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Question 851082: 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.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
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,
x%5E2+%2B+%28x+%2B+5%29%5E2+=+75%5E2
x%5E2+%2B+x%5E2+%2B+10%2Ax+%2B+25+=+5625
i.e. 2%2Ax%5E2+%2B+10%2Ax+-+5600+=+0 or Dividing it by 2 throughout
x%5E2+%2B+5%2Ax+-+2800+=+0
This can be solved using the quadratic solver as shown below.



 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-2800+=+0) has the following solutons:
  
  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca
  
  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.
  
  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A-2800=11225.
  
  Discriminant d=11225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+11225+%29%29%2F2%5Ca.
  
    x%5B1%5D+=+%28-%285%29%2Bsqrt%28+11225+%29%29%2F2%5C1+=+50.4740502510427
    x%5B2%5D+=+%28-%285%29-sqrt%28+11225+%29%29%2F2%5C1+=+-55.4740502510427
    
    Quadratic expression 1x%5E2%2B5x%2B-2800 can be factored:
  1x%5E2%2B5x%2B-2800+=+1%28x-50.4740502510427%29%2A%28x--55.4740502510427%29
  Again, the answer is: 50.4740502510427, -55.4740502510427.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-2800+%29



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 highlight%2850.5%29, highlight%2855.5%29, and highlight%2875%29 inches respectively.

:)