If two sides of the triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?
B. 1 only
C. 2 only
D. 2 and 3 only
E. 1, 2 and 3
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
2+5+x=19, x=12,sides 2,5,12,
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)
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