document.write( "Question 456884: The sides of a length of a triangle are x, x+4, and 20, where 20 is the longest side. For which range of values is x an acute triangle \n" ); document.write( "

Algebra.Com's Answer #313514 by spacesurfer(12) $\"\"$ $\"About$

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First, a right triangle is the breaking point for acute vs obtuse triangle. We find for what x we have a right triangle. There are two scenarios:\r
\n" ); document.write( "\n" ); document.write( "Case 1) x and (x+4) are the two feet and 20 is the hypotenuse or
\n" ); document.write( "Case 2) x and 20 are the two feet and (x+4) is the hypotenuse\r
\n" ); document.write( "\n" ); document.write( "Note that 20 and (x+4) cannot be the 2 feet since x < x+4.\r
\n" ); document.write( "\n" ); document.write( "Case 1) $\"x%5E2+%2B+%28x%2B4%29%5E2+=+20%5E2\"$ --> The solution is x = 12 after discarding -16 as a solution.
\n" ); document.write( "Case 2) $\"x%5E2+%2B+20%5E2+=+%28x%2B4%29%5E2\"$ --> x = 48.\r
\n" ); document.write( "\n" ); document.write( "Hence, 12 < x < 48 since, when x = 12, we have a right triangle with sides 12, 16, 20; and when x = 48, we have another right triangle with side 20, 48, 52. \n" ); document.write( "

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