What is the perimeter of isosceles triangle LMN?

[Vincen]

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 OA is E.

If we use both statements together we can find the perimeter of the triangle. Am I wrong?

[ErikaPrepScholar]

Hey Vincen,

The big issue here is that we know that the triangle is isosceles, but we don't know which two sides are the same. We know with both statements that LM and MN are different. But we don't know whether LN is the same length as LM (4) or the same length as MN (4√2). If LN and LM are the same, the perimeter is 4 + 4 + 4√2. If LN and MN are the same, the perimeter is 4 + 4√2 + 4 √2. Not the same.

So even with both statements, we don't know the perimeter of the triangle.