# Thread: Is my reasoning correct?

1. ## Is my reasoning correct?

The question states:
The length of two sides of a trangle are (x-2) and (x+2), where x>2. Which of the following ragnes includes all and only the possible values of the thrid side Y?
A)0<y<x
B)0<y<2x
C)2<Y<x
D)4<Y<x
E)4<Y<2x

I got the answer choice E. Apparently, though, the answer resulted to be B. What i dont get is, the question says "Which of the following ragnes includes all and only the possible values of the thrid side Y?" However, in the ranges between 0 and 2x, there are values that will be incorrect. Considering x=5, B will not satisfy it. If my reasoning is wrong, please teach me the correct way to look at the problem. Thank you guys

2. The possible values for the third side of a triangel given the other two sides is represented by this:

$\displaystyle (difference\; \; of \; \;other \; \;2 \; \;sides) < y < (sum \; \; of \; \; other \; \; two \; \; sides)$

Thus,

$\displaystyle (x+2)-(x-2)<y<(x-2)+(x+2)$

$\displaystyle x+2-x+2<y<x-2+x+2$

$\displaystyle 4<y<2x$