document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #48803 by funmath(2933) $\"\"$ $\"About$

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The legs in a right triangle equal 3x and 20. The hypotenuse of the triangle is 4x-1. Find the value of x.
\n" ); document.write( "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.
\n" ); document.write( " $\"%284x-1%29%5E2=%283x%29%5E2%2B%2820%29%5E2\"$
\n" ); document.write( " $\"16x%5E2-8x%2B1=9x%5E2%2B400\"$
\n" ); document.write( " $\"16x%5E2-9x%5E2-8x%2B1-400=9x%5E2-9x%5E2%2B400-400\"$
\n" ); document.write( " $\"7x%5E2-8x-399=0\"$ 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.
\n" ); document.write( " $\"7x%5E2%2B49x-57x-399=0\"$
\n" ); document.write( " $\"7x%28x%2B7%29-57%28x%2B7%29=0\"$
\n" ); document.write( " $\"%287x-57%29%28x%2B7%29=0\"$ Let each parentheses = 0 and solve for x.
\n" ); document.write( " $\"7x-57=0\"$ or $\"x%2B7=0\"$
\n" ); document.write( " $\"7x-57%2B57=0%2B57\"$ or $\"x%2B7-7=0-7\"$
\n" ); document.write( " $\"7x=57\"$ or $\"x=-7\"$
\n" ); document.write( " $\"7x%2F7=57%2F7\"$ or $\"x=-7\"$
\n" ); document.write( " $\"x=57%2F7\"$ or $\"x=-7\"$
\n" ); document.write( "Throw out the negative answer because a triangle can't have a negative side.
\n" ); document.write( " $\"highlight%28x=57%2F7%29\"$
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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