SOLUTION: I need Help Please!! The triangle inequality states that the sum of any two sides of a triangle must be bigger than the third side. The following triangle RST has sides of l

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Question 949734: I need Help Please!!
The triangle inequality states that the sum of any two sides of a triangle must be bigger than the third side.
The following triangle RST has sides of length x. 2x, 10 as shown.
A)Find the three inequalities, which must be true based on the sides of the triangle.
B)Write a compound inequality on your results above.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Simply use the given numbers for the side lengths and follow what the theorem says.

system%28x%2B2x%3E10%2C2x%2B10%3Ex%2Cx%2B10%3E2x%29

That is how to start. Simplify each inequality for x, and accept only the POSITIVE inequality solution. You are looking for an intersection.

system%283x%3E10%2C2x%3E-10%2C10%3Ex%29

system%28x%3E10%2F3%2Cx%3E-5%2Cx%3C10%29

Obviously you cannot use anything between -5 and 0. That second inequality is not very helpful now. The statements which work are combined as highlight%2810%2F3%3Cx%3C10%29.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The following triangle RST has sides of length x, 2x, 10+as shown.
A) Find the three inequalities, which must be true based on the sides of the triangle.
1. x%3C2x%2B10
2. 2x%3Cx%2B10
3. 10%3C2x%2Bx
B) Write a compound inequality on your results above.
Remember that side lengths also need to be positive. Thus, each side must
be greater than zero. Take the smallest side length to ensure this.
2x+%3C+x%2B10=> 2x-x+%3C+10=>x+%3C+10
10+%3C+2x%2Bx=>10+%3C+3x=>10%2F3%3C+x
10%2F3+%3C+x+%3C10