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

Algebra ->  Pythagorean-theorem -> SOLUTION: The legs in a right triangle equal 3x and 20. The hypotenuse of the triangle is 4x-1. Find the value of x.       Log On


   

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) About Me  (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: highlight%28c%5E2=a%5E2%2Bb%5E2%29, where c=hypotenuse and a and b are leags of a right triangle.
%284x-1%29%5E2=%283x%29%5E2%2B%2820%29%5E2
16x%5E2-8x%2B1=9x%5E2%2B400
16x%5E2-9x%5E2-8x%2B1-400=9x%5E2-9x%5E2%2B400-400
7x%5E2-8x-399=0 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.
7x%5E2%2B49x-57x-399=0
7x%28x%2B7%29-57%28x%2B7%29=0
%287x-57%29%28x%2B7%29=0 Let each parentheses = 0 and solve for x.
7x-57=0 or x%2B7=0
7x-57%2B57=0%2B57 or x%2B7-7=0-7
7x=57 or x=-7
7x%2F7=57%2F7 or x=-7
x=57%2F7 or x=-7
Throw out the negative answer because a triangle can't have a negative side.
highlight%28x=57%2F7%29
Happy Calculating!!!

Answer by Edwin McCravy(20054) About Me  (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