We know that the sum of any two sides of a triangle must be greater than the third. So we know, before even looking at the statements, thatcfarrera wrote:Triangle A has sides:
1. 4x-3
2. 2x+1
3. x+8
What is the perimeter of triangle A?
(1) Triangle A is an isosceles
(2) x+8 is the greatest side
Answer is D, help!! I do not get the answer....
4x - 3 + 2x + 1 > x + 8
x > 2
and
2x + 1+ x + 8 > 4x - 3
12 > x
(the third combination of sides doesn't give us anything useful). That is, 2 < x < 12.
Considering Statement 1, which pair of sides could be equal? 2x + 1 cannot be equal to 4x - 3, because then x = 2, and we know that's impossible from the analysis above. Still, the other pairs could be equal:
4x - 3 = x + 8
x = 11/3
or
2x + 1 = x + 8
x = 7
You get a different perimeter for each x, so the Statement is not sufficient.
Considering Statement 2, we know that x + 8 is greater than either of the other two sides, from which we can produce two inequalities:
x + 8 > 2x + 1
x < 7
and
x+ 8 > 4x - 3
x < 11/3
So we know that x < 11/3, and from above, we know that x > 2. Still, we can't determine the perimeter, since we only have a range of values for x. So the Statement is not sufficient.
The two Statements are clearly contradictory, so it's impossible to consider both of them together, which means there's something wrong with the question. Where is it from?
