When the statements are combined, apply the THIRD-SIDE RULE:jain2016 wrote:What is the perimeter of isosceles triangle LMN?
1) Side LM has a length of 4
2) side MN has a length of 4√2.
The length of the third side of a triangle must be GREATER THAN THE DIFFERENCE BETWEEN THE LENGTHS OF THE OTHER 2 SIDES and LESS THAN THE SUM OF THE LENGTHS OF THE OTHER 2 SIDES.
According to the rule above:
4√2 - 4 < LN < 4√2 + 4.
Thus:
It's possible that LN = 4, in which case the perimeter = 4 + 4 + 4√2.
It's possible that LN = 4√2, in which case the perimeter = 4 + 4√2 + 4√2.
Since the perimeter can be different values, INSUFFICIENT.
The correct answer is E.
Note:
The problem does not require that LMN be a right triangle.
