prep question

[vgp]

If two sides of the triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

1. 9
2. 15
3. 19

A. None
B. 1 only
C. 2 only
D. 2 and 3 only
E. 1, 2 and 3

[clock60]

i got A-none.
let it be x the last side of the triangle
2+5+x=9, and x=2, so triangle with sides 2,2,5
according to the inequality of triangle the lengh of any side of triangle does not exceed the sun of the last two
and in out case 5>2+2 so this triangle does not exist

2+5+x=15, x=8, sides 2,5,8
8>2+5

2+5+x=19, x=12,sides 2,5,12,
12>2+2
so none-A

[sheelanadh]

i got A-none.
let it be x the last side of the triangle
2+5+x=9, and x=2, so triangle with sides 2,2,5
according to the inequality of triangle the lengh of any side of triangle does not exceed the sun of the last two
and in out case 5>2+2 so this triangle does not exist

2+5+x=15, x=8, sides 2,5,8
8>2+5

2+5+x=19, x=12,sides 2,5,12,
12>2+2
so none-A

Thank you clock60.But I want little bit explanation for this.

[MBAchase]

if you KNOW two sides of a triangle, then
DIFFERENCE < third side < SUM

this can be derived directly from the triangle inequality (the thing discussed above), but it's worth memorizing separately; the last thing you want to do on a 2-minute problem is start deriving new rules.

in this problem, this rule immediately yields
5 - 2 < third side < 5 + 2
3 < third side < 7
10 < perimeter < 14 (add 7 to both sides)
done

[DMoney]

Why did you arbitrarily add 7 to each side?

[IIMPUNE]

7 = 5 + 2 i.e Sum of Given Sides