SOLUTION: 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? (F) 4 meters (G) 5 meters (H) 11 meters (J) 12 meters

Algebra ->  Pythagorean-theorem -> SOLUTION: 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? (F) 4 meters (G) 5 meters (H) 11 meters (J) 12 meters      Log On


   

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?
(F) 4 meters (G) 5 meters (H) 11 meters (J) 12 meters
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
L= length (in meters) of the longest side
S= length (in meters) of the shortest side (or one of the two shorter sides, if isosceles)
M= length (in meters) of the other side.
For that triangle to be obtuse, we need
S%5E2%2BM%5E2%3CL%5E2 .

If the 9 meter side is the longest side, and the length of the other side is x meters,
x%5E2%2B7%5E2%3C9%5E2<-->x%5E2%2B49%3C81<-->x%5E2%3C81-49<-->highlight%28x%5E2%3C32%29 .

If the longest side is the unknown side, measuring x meters,
7%5E2%2B9%5E2%3Cx%5E2<-->49%2B81%3Cx%5E2<-->highlight%28x%5E2%3E130%29 .

4%5E2=16%3C32 so a 4 meter shortest side is an option;
5%5E2=25%3C32 so a 4 meter shortest side is an option;
12%5E2=144%3E130 so a 12 meter longest side is an option, but
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 .