# Thread: [SOLVED] Rational Restrictions of a Triangle?

1. ## [SOLVED] Rational Restrictions of a Triangle?

Hi, i have a question on the restrictions of this triangle. The side lengths for a triangle are 2x+3, 3x-5 an x+5. The triangle is scalene. I've included a picture below. The restrictions on a triangle can't be as simple as solving for x for each side can it? The question asks: For what values of x is the triangle possible?

Thanks.

2. Originally Posted by demo1
Hi, i have a question on the restrictions of this triangle. The side lengths for a triangle are 2x+3, 3x-5 an x+5. The triangle is isosceles. I've included a picture below. The restrictions on a triangle can't be as simple as solving for x for each side can it? The question asks: For what values of x is the triangle possible?

Thanks.
no picture

what two sides are equal?

3. Sorry, the triangle is scalene. And I've just uploaded the picture. Thanks for pointing it out.

4. any two sides of a triangle must sum to be greater than the third side ...

(2x+3) + (3x-5) > x+5

(2x+3) + (x+5) > 3x-5

(3x-5) + (x+5) > 2x+3

solve all three inequalities and find the intersection of their solution sets to determine all possible values for x.

5. I think i got it. Thanks!