document.write( "Question 166039: The area of a triangle is 56ft^2. If the base is 9 ft more than the altitude, find the length of the base and the altitude. \n" ); document.write( "

Algebra.Com's Answer #122426 by orca(409) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x be the altitude, then the base is x + 9.
\n" ); document.write( "Its area is $\"%281%2F2%29%2Ax%28x%2B9%29\"$
\n" ); document.write( "As its area is 56, we have
\n" ); document.write( " $\"%281%2F2%29%2Ax%28x%2B9%29=56\"$
\n" ); document.write( "Solving for x, we have
\n" ); document.write( " $\"x%28x%2B9%29=112\"$
\n" ); document.write( " $\"x%5E2%2B9x=112\"$
\n" ); document.write( " $\"x%5E2%2B9x-112=0\"$
\n" ); document.write( " $\"x+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A1%2A%28-112%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"x+=+%28-9+%2B-+sqrt%28+529+%29%29%2F2+\"$
\n" ); document.write( " $\"x+=+%28-9+%2B-+23%29%2F2+\"$
\n" ); document.write( "So
\n" ); document.write( " $\"x+=+%28-9+%2B+23%29%2F2=7+\"$
\n" ); document.write( "Or
\n" ); document.write( " $\"x+=+%28-9+-+23%29%2F2=-16\"$ (reject this negative root)
\n" ); document.write( "Thus the length of the altitude is 7, and the length of the base is x+9 = 7+9=16.
\n" ); document.write( " \n" ); document.write( "

\n" );