SOLUTION: The legs in a right triangle equal 3x and 20. The hypotenuse of the triangle is 4x-1. Find the value of x.

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Question 68566: The legs in a right triangle equal 3x and 20. The hypotenuse of the triangle is 4x-1. Find the value of x.
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
The legs in a right triangle equal 3x and 20. The hypotenuse of the triangle is 4x-1. Find the value of x.
The pythagorean theorem says: , where c=hypotenuse and a and b are leags of a right triangle.



I am factoring using the ac or grouping method. You replace the middle number by two numbers that multiply to give you (7)(-399)=2793, but add together to give you the middle number -8 then factor by grouping.


Let each parentheses = 0 and solve for x.
or
or
or
or
or
Throw out the negative answer because a triangle can't have a negative side.

Happy Calculating!!!
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The legs in a right triangle equal 3x and 20. 
The hypotenuse of the triangle is 4x - 1. 
Find the value of x.

            a = 3x
            b = 20
            c = 4x - 1

      a² + b² = c²
(3x)² + (20)² = (4x - 1)²
    9x² + 400 = (4x - 1)(4x - 1)

Use FOIL on the right side

    9x² + 400 = 16x² - 4x - 4x + 1

    9x² + 400 = 16x² - 8x + 1

            0 = 16x² - 8x + 1 - 9x² - 400

            0 = 7x² - 8x - 399

That will factor as

            0 = (x + 7)(7x - 57)

         x + 7 = 0 gives x = -7
       7x - 57 = 0 gives x = 57/7

Since a triangle cannot have negative
sides, we discard x = -7.  So the answer
is x = 57/7 

Edwin
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