# Question: ABC Perimeter

## Comment on ABC Perimeter

### Isn't it impossible for the

Isn't it impossible for the unknown side to be 4 due to the fact that the hypotenuse (4) is opposite the biggest angle therefore making it the longest possible side. And then that making it so that the unknown side has to be 3

### There's nothing in the

There's nothing in the question that states ABC is a right triangle? So, there isn't a hypotenuse to speak of.

Are you confusing "isosceles triangle" with "right triangle"?

### Sir how can the unknown

Sir how can the unknown length be 4? and why not just 3?
if length is 4 then the angles on the opposite sides wont match.
In this way we can changed any figure in any way and the answer will yield D, and by the looks of it, 4 is the longest side and 3 is the shortest length on both sides.

### "...by the looks of it, 4 is

"...by the looks of it, 4 is the longest side and 3 is the shortest length on both sides"

The diagrams in Quantitative Comparison questions are not necessarily drawn to scale. So, in this question, we can't make assumptions about which two sides are equal.

For more on what assumptions we can and cannot make, watch: https://www.greenlighttestprep.com/module/gre-geometry/video/863

### Hello! I was confused because

Hello! I was confused because, I thought below method was to solve the problem.
|A-B| < 3rd side < A+B

I guess for Isosceles, above method is not qualified? This only works on right triangle??

### The rule, |A-B| < 3rd side <

The rule, |A-B| < 3rd side < A+B, applies to ALL triangles.
So, for this question, we know that: |4-3| < 3rd side < 4+3

However, in the given question, we're also told that the triangle is isosceles.
So, the 3rd side must have length 3 or 4 (to match one of the given sides)

Cheers,
Brent

### Understood perfectly! Thank

Understood perfectly! Thank you

### Are we going to be told which

Are we going to be told which diagrams are drawn to scale and which aren't

### Unfortunately no. We won't be

Unfortunately no. We won't be told which diagrams are drawn to scale and which aren't. So, we must assume that all diagrams are NOT drawn to scale.

For more on what can and cannot be assumed, watch https://www.greenlighttestprep.com/module/gre-geometry/video/863

Cheers,
Brent

### Hi Brent

Hi Brent
In the video at 00:51 you have calculated the permiter when BC=3 then 3+3+4=13 should be there
BC=4 then 4+4+3=11

Am I calculating the perimeter in a wrong way
Thanks

### When BC = 3, then the three

When BC = 3, then the three lengths are 3, 3 and 4.
You're correct to say that the perimeter = 3 + 3 + 4
However, 3 + 3 + 4 = 10 (not 13)

Cheers, Brent

### Hi Brent if BC is 4, the will

Hi Brent if BC is 4, the will that be legitimate to the rule
The grater angle has longest sides A<B<C a<b<c

### Sorry Vineet. I'm not sure

Sorry Vineet. I'm not sure what you're asking. Can you rephrase your question?

### Sorry Vineet. I'm not sure

Sorry Vineet. I'm not sure what you're asking. Can you rephrase your question?

### Hello Brent we have a rule

Hello Brent we have a rule that says for a given triangle longest side has largest angle if the BC is 3 in our problem. Will that rule still applies, if so how?

### If BC = 3, then the three

If BC = 3, then the three lengths are 3, 3 and 4, which means AC is the longest side, which means angle B is the biggest angle.

If BC = 4, then the three lengths are 3, 4 and 4, which means AC and BC are tied for the longest side, which means angle A and angle B are tied for the biggest angle.

Having said all of that, the relationship between angles and lengths doesn't really apply here. All we need to know is that an isosceles triangle has two equal sides, since this is all we need to calculate the perimeter.

Does that help?

### Since we have sides measure

Since we have sides measure of 3 & 4. Can't we assume that its a 3-4-5 triangle? in that case 3+4+5=12....

### There are infinitely many

There are infinitely many triangles that have sides with lengths 3 and 4.
IF the angle between those two sides is 90°, then the third side will have length 5.
Otherwise all we can say is: 1 < length of 3rd side < 7 (after applying the property described here https://www.greenlighttestprep.com/module/gre-geometry/video/860)

### Oh, I see. So, it needs to be

Oh, I see. So, it needs to be a right triangle. Thank you very much.