document.write( "Question 1019981: The lengths of two sides of an obtuse triangle are 7 meters and 9 meters. Which could NOT be the length of the third side?
\n" ); document.write( "(F) 4 meters (G) 5 meters (H) 11 meters (J) 12 meters \n" ); document.write( "

Algebra.Com's Answer #635914 by KMST(5328) $\"\"$ $\"About$

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$\"L\"$ = length (in meters) of the longest side
\n" ); document.write( " $\"S\"$ = length (in meters) of the shortest side (or one of the two shorter sides, if isosceles)
\n" ); document.write( " $\"M\"$ = length (in meters) of the other side.
\n" ); document.write( "For that triangle to be obtuse, we need
\n" ); document.write( " $\"S%5E2%2BM%5E2%3CL%5E2\"$ .
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\n" ); document.write( "If the $\"9\"$ meter side is the longest side, and the length of the other side is $\"x\"$ meters,
\n" ); document.write( " $\"x%5E2%2B7%5E2%3C9%5E2\"$ <--> $\"x%5E2%2B49%3C81\"$ <--> $\"x%5E2%3C81-49\"$ <--> $\"highlight%28x%5E2%3C32%29\"$ .
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\n" ); document.write( "If the longest side is the unknown side, measuring $\"x\"$ meters,
\n" ); document.write( " $\"7%5E2%2B9%5E2%3Cx%5E2\"$ <--> $\"49%2B81%3Cx%5E2\"$ <--> $\"highlight%28x%5E2%3E130%29\"$ .
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\n" ); document.write( " $\"4%5E2=16%3C32\"$ so a 4 meter shortest side is an option;
\n" ); document.write( " $\"5%5E2=25%3C32\"$ so a 4 meter shortest side is an option;
\n" ); document.write( " $\"12%5E2=144%3E130\"$ so a 12 meter longest side is an option, but
\n" ); document.write( " $\"32%3C11%5E2=121%3C130\"$ means that an obtuse triangle with sides measuring 7 and 9 meters cannot have a third side measuring $\"highlight%2811meters%29\"$ .
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