document.write( "Question 510706: i need to find the lengths of the three sides of the triangle given that the sides are x-5, 2x, and 2x+1. i know the answer is x=12, but i do not know how to get it using algebra \n" ); document.write( "

Algebra.Com's Answer #341857 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
The problem, as stated, is not solvable!
\n" ); document.write( "If the triangle is a right triangle, or an equilateral triangle, you have to say so. Let's assume that it's a right triangle so we can use the Pythagorean theorem: $\"c%5E2+=+a%5E2%2Bb%5E2\"$
\n" ); document.write( "For any positive value of x, 2x+1 has to be the largest side and thus the hypotenuse (c) so...
\n" ); document.write( " $\"%282x%2B1%29%5E2+=+%28x-5%29%5E2%2B%282x%29%5E2\"$ Simplify.
\n" ); document.write( " $\"4x%5E2%2B4x%2B1+=+x%5E2-10x%2B25%2B4x%5E2\"$
\n" ); document.write( " $\"4x%5E2%2B4x%2B1+=+5x%5E2-10x%2B25\"$ Subtract 4x^2 from both sides.
\n" ); document.write( " $\"4x%2B1+=+x%5E2-10x%2B25\"$ Subtract 4x from both sides.
\n" ); document.write( " $\"1+=+x%5E2-14x%2B25\"$ Subtract 1 from both sides.
\n" ); document.write( " $\"x%5E2-14x%2B24+=+0\"$ Solve by factoring.
\n" ); document.write( " $\"%28x-2%29%28x-12%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"x-2+=+0\"$ or $\"x-2+=+0\"$
\n" ); document.write( " $\"x+=+2\"$ or $\"x+=+12\"$ Discard $\"x+=+2\"$ as an invalid solution because x = 2 will give you a negative (x-5 = -3) side length.
\n" ); document.write( "Answer is $\"x+=+12\"$ \n" ); document.write( "

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