document.write( "Question 1191818: The length of the longest side is the integer given. What value(s) of x make the triangle? x-4 , x+7, 45 ; Acute triangle \n" ); document.write( "

Algebra.Com's Answer #823666 by greenestamps(13198) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Finding the maximum possible value of x is easy. It is given that the longest side is 45, so

\n" ); document.write( " $\"x%2B7%3C45\"$
\n" ); document.write( " $\"x%3C38\"$

\n" ); document.write( "To determine the smallest possible values of x, note that the triangle is a right triangle if

\n" ); document.write( " $\"%28x-4%29%5E2%2B%28x%2B7%29%5E2=45%5E2\"$

\n" ); document.write( "So the triangle is acute if

\n" ); document.write( " $\"%28x-4%29%5E2%2B%28x%2B7%29%5E2%3E45%5E2\"$

\n" ); document.write( " $\"%28x-4%29%5E2%2B%28x%2B7%29%5E2=45%5E2\"$
\n" ); document.write( " $\"x%5E2-8x%2B16%2Bx%5E2%2B14x%2B49=2025\"$
\n" ); document.write( " $\"2x%5E2%2B6x%2B65=2025\"$
\n" ); document.write( " $\"2x%5E2%2B6x-1960=0\"$
\n" ); document.write( " $\"x%5E2%2B3x-980=0\"$

\n" ); document.write( "Use the quadratic formula to find

\n" ); document.write( " $\"x=%28-3%2Bsqrt%283929%29%29%2F2\"$ = 29.805 to 3 decimal places

\n" ); document.write( "So the triangle with longest side 45 and the other two sides x-4 and x+7 is acute for any value greater than (approximately) 29.805 and less than 38.

\n" ); document.write( "ANSWER: 29.805 < x < 38
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );