Posted by AnnaMarie on Monday, March 3, 2008 at 10:30pm.
1. The sides of a triangle have lenghts x, x+4, and 20. Specify those values of x for which the triangle is acute with the longest side 20.
2. use the information to decide if triangle ABC is acute, right, or obtuse.
AC=13, BC= sq. rt. 34, CD=3
>>i know this is obtuse but why?
3. If x and y are positive numbers with x>y, show that a triangle with sides of lenghts 2xy, x^2  y^2, and x^2 + y^2 is always a right triangle.
I HATE WORD PROBLEMS!! Thanks for helping =]

Geometry (#1 of 3)  drwls, Tuesday, March 4, 2008 at 12:47am
A right triangle with largest side 20 would have
x^2 + (x+4)^2 = 400
x^2 + 4x + 8 = 200
x^2 + 4x 192 = 0
(x12)(x+16) = 0
The only root that makes sense (by being positive) is x = 12. That means that you have a right triangle if the sides are 12 and 16. (The x = 12 case). If x>12, the triangle is acute, meaning thet the largest angle is less than 90 degrees. If x<12, it is obtuse. You should be able to convince yourself of that by drawing the figure or by using the law of cosines.

Geometry  drwls (#2 of 3), Tuesday, March 4, 2008 at 6:39am
It is not obtuse; it is impossible because one side is longer than the sum of the other two.
You also posted this problem separately. I gave a more complete answer there.

Geometry (#3 of 3)  drwls, Tuesday, March 4, 2008 at 6:44am
Let the first side be A, the second side b and the third side C.
Note that
(x^2  y^2)^2 + (2xy)^2 = x^4 + 2x^2y^2 + y^2 = (x^2 + y^2)^2
Therefore the relationship A^2 + B^2 = C^2 is obeyed. This is only true for a right triangle.
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