# GRE Math practice question. Possible wrong answer?

So I was going through questions in a GRE prep book and I'm just convinced this answer is wrong but I understand the likelihood is very slim. Can someone check my work and explain why I am wrong?

So I am given this isosceles triangle and I am told the measure of the angles are expressed by 2x+y=180. Since the triangle is isosceles I know the perimeter would either be represented by 7+7+4=18 or 7+4+4=15. Now from here can't I drop an altitude from R and figure out which perimeter correctly represents the triangle?

I showed my work however the answer key says the relationship between Quantity A and Quantity B cannot be determined.

• Can you post an image of the original question, what are you given to start with? Just that the triangle is isoceles, it has two angles x that are equal, y that isn't... where is the 7 in your (7+7+4) coming from? In your question, at the end put down a "-------" and underneath it, write exactly what is given in the question – frogeyedpeas Jul 10 '16 at 2:26
• yeah let me add the image I just scribbled all around it lol – Lil Jul 10 '16 at 2:28
• I think its quantity A is greater but the book says the relationship cannot be determined – Lil Jul 10 '16 at 2:32
• The problem is that the picture implies that $7$ is the duplicated value, but nothing in the body of the question implies that. So yes, the triangle could be $4,4,7$ or $4,7,7$, so it could have perimeter $15$ or $18$. Basically, this is a trick question, reminding you that you should not draw any inference from the picture of the problem, except the specific lengths (4,7) listed and the fact given in the text. – Thomas Andrews Jul 10 '16 at 2:34

The problem is that the picture implies that $7$ is the duplicated value, but nothing in the body of the question implies that. So yes, the triangle could be $4,4,7$ or $4,7,7$, so it could have perimeter $15$ or $18$.
The picture is not of a $4,4,7$ triangle, because it is not obtuse, but the picture is not something from which you should use when making geometric inferences.
• @Lil Dropping the perpendicular does not necessarily bisect the $4$ side - if it did, then you could conclude the third side is $7$ – Thomas Andrews Jul 10 '16 at 2:41
• Dropping a perpendicular from the vertex where the equal sides meet resolves nothing. If the equal sides have length $4$ then the length of the perpendicular is $\dfrac{\sqrt{15}}{2}$, if the equal sides have length $7$ then the length of the perpendicular is $3\sqrt{5}$. – John Wayland Bales Jul 10 '16 at 2:55
• You don't have any freaking idea where the altitude will land or even if it will land inside the triangle. The best you could do is you'd get $w \pm v =4$ and $7=\sqrt {x^2 +w^2}$ and the third $4 or 7=\sqrt {x^2+v^2}$. Which will give you two possible results that will not help you. (Oh, it will tell you if the third side is 4 whether the altitude will be in or out of the triangle-- but that's all). You can not resolve from this. – fleablood Jul 10 '16 at 6:53