ardz24 wrote:Is the perimeter of a triangle greater than 1?
(1) Two of the heights are less than 1/3
(2) One of the heights is greater than 1/2
What's the best way to determine whether statement 1 is sufficient? Can any experts explain?
Remember the two rules for a triangle.
1. The sum of any two sides is GREATER than the third side.
2. The difference of any two sides is LESS than the third side.
Let's see the statements.
(1) Two of the heights are less than 1/3.
Since the two of the heights are less than 1/3, their sum is less than 2/3, thus the third is less than 2/3.
=> Perimeter of the triangle < 1/3 + 1/3 + 2/3 (= 4/3 = 1 1/3). The perimeter may or may not be less than 1. Insufficient.
(2) One of the heights is greater than 1/2.
Since one of the heights is greater than 1/2, the sum of the other two sides must be greater than 1/2.
=> Perimeter = One side + Sum of the other two sides > 1/2 + 1/2 => Perimeter > 1. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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