SOLUTION: The sides of a triangle have lengths 2x+2, 4x and 5x+1. The longest side of the triangle has a length of 5x-1. For what values of x is the triangle obtuse?

Algebra ->  Pythagorean-theorem -> SOLUTION: The sides of a triangle have lengths 2x+2, 4x and 5x+1. The longest side of the triangle has a length of 5x-1. For what values of x is the triangle obtuse?      Log On


   

Question 1066304: The sides of a triangle have lengths 2x+2, 4x and 5x+1. The longest side of the triangle has a length of 5x-1. For what values of x is the triangle obtuse?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
AS GIVEN and described, 5x-1%3E5x%2B1
and a strep from that GIVEN information is
5x-1%2B%28-5x%29%3E5x%2B1%2B%28-5x%29
-1%3E1-----------a false statement.


The first THREE expressions should work this way:
%285x%2B1%29%5E2%3E%282x%29%5E2%2B%284x%29%5E2

25x%5E2%2B10x%2B1%3E4x%5E2%2B16x%5E2

25x%5E2%2B10x%2B1%3E20x%5E2

5x%5E2%2B10x%2B1%3E0

Critical x-values:
%28-10%2B-+sqrt%28100-4%2A5%2A1%29%29%2F%282%2A5%29

%28-10%2B-+sqrt%2880%29%29%2F10

%28-10%2B-+sqrt%282%2A2%2A2%2A2%2A5%29%29%2F10

%28-10%2B-+4%2Asqrt%285%29%29%2F10

highlight_green%28-1%2B-+%282%2F5%29sqrt%285%29%29


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You should check also to be sure you know what values for x will make the lengths 2x+2, 4x, and 5x+1, POSITIVE VALUES. Note, because of 4x one of the sides, highlight_green%28x%3E0%29 necessary.

Look at -1%2B%282%2F5%29sqrt%285%29;
-0.105572
which is the right-hand critical value of x, negative, and therefore will not work for 4x;
The values for x to the left of the left-hand critcal value will also not be acceptable, because they are negative. The interval between the two critical x-values neither will work; the inequality will fail as well as side length 4x being negative.

SOLUTION:
highlight%28x%3E0%29