What is the perimeter of the triangle in the figure above?

It is clear from the figure that y=z and x=y because they form opposite angle at the vertex. This goes on to prove x=y=z.
Also, notice that the interior angle at the vertex J is 2x because they are also opposite angles and hence they must be equal.

Hence, the three angles are 2x, y , z and x=y=z.

2x+x+x=180
4x=180
x=180/4=45.

.


Considering the information provided.

(1) The side across from interior angle z measures 2.

We have one side and we can easily find the other sides as we know 45-45-90 right triangle has a 1:1:root(2) side ratio. We can find the perimeter easily.

HENCE, SUFFICIENT.

(2) 2x > y

This doesn't provide us with any extra information but only goes on to state the obvious data that is given in the diagram.
Hence, insuffucient.

HENCE, THE ANSWER IS A.



Leave me a KUDO if this explanation makes sense to you.

I do not see anything in the question that gets a 45-45-90 triangle. x could be equal to 40 and 2x=80, leaving y to be 60. Would that be a possibility?

Thanks!

Notice that angles in the triangle boil down to x, x and 2x. (Please refer to my explanation of the question above.)

Now taking the situation you have provided. "if x = 20 and 2x = 80 leaving y to be 60." It goes on to contradict x=y. and y=z which is the first thing we proved to begin our solution. Hence it is incorrect.

When dealing with GEOMETRY always look closely at the figure and find out all the values and cases you can without breaking any rule.

1. Opposite angles formed by two straight lines at vertex are equal.
2. Sum of all three angles is 180.

Using just these two properties we can easily proceed with the solution.

TIP -- Always consider everything a Geometrical figure has to offer. Never start a Geometrical question with a guess or an assumption.

Let me know if there is something else I can help you with in this question.



Please leave a KUDO if you found this explanation helpful.

Bunuel
VeritasPrepKarishma

I have a doubt - kindly see my image and reply .


Statement 1 says
The side across from interior angle z measures 2


I have a ques -> we can have 2 cases => case 1 KL =2 , so JK = √2 . yes we can find perimeter, which is => P1 =2+2√2
case 2 => JK = 2, now KL = 2√2 => perimeter P2 = 4+2√2

Here P1 is not equal to P2
therefore multiple solution ->

A should be rejected..


KINDLY share your views and enlighten me.

JKL is a 45-45-90 right triangle (x = 45 degrees), where KL is the hypotenuse (across 2x = 90 degree angle). So, the ratio of the sides is \(JL:JK:KL=1:1:\sqrt{2}\)

The side across angle z is side JL. So, \(JL = JK = 2\) and \(KL = 2\sqrt{2}\).

Does this make sense?

Thanks Bunuel -> only thing i was not aware of term across from -> If i knew that the term across from means opposite to, I would have not done this wrong.

Anyways thanks again.

side across from interior angle z measures 2,which side are we referring to in this case?

The side across from interior angle z, refers to side opposite to angle z, so to side JL.

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