Sides of a triangle

[DaveC426913]

Homework Statement

This isn't actually homework; its one of them dumb Facebook puzzles.

Relevant Equations

A+B+C=p

This is one of those dumb Facebook puzzles. The only reason I'm posting it here is because I'm beginning to question my sanity.


450 responses so far have all provided the same answer. Not a single user has posted the other correct answer.

A triangle has sides that are consecutive even integers.
The perimeter of the triangle is 30 inches.
What is the length of the short side?

A bunch of people said 9 (because they can't read good).
Most people said 8: (12, 10 ,8) A lot of those people showed their work that resolved to 8 as a solution.

Not a single one of them has stumbled across the other solution 4: (14,12,4).

Am I bonkers?

Man, there is nothing like writing up a question to get you to you see the solution.
In triple checking my post I now see my error:

A triangle has sides that are consecutive even integers.

I assumed "sides" was referring to only the two, not all three.
My answer is only valid if you allow for, and take advantage of, that slight ambiguity.


It should say: A triangle has all three sides that are consecutive even integers.

 

[anuttarasammyak]

I interpret
2(3n+3)=30

 

[DaveC426913]

I interpret
2(3n+3)=30

I am not sure how you arrive at that formula. It results in n=4, which does not satisfy the strict interpretation of the puzzle.

 

[phinds]

I interpret
2(3n+3)=30

HUH? That would give n=4, so the sides would be 4,5,6 --- in what world does that add up to 30?

 

[DaveC426913]

HUH? That would give n=4,

Yes.

so the sides would be 4,5,6

I'm not sure how you arrived at those other two numbers. His formula doesn't produce 5 and 6.

 

[anuttarasammyak]

HUH? That would give n=4, so the sides would be 4,5,6 --- in what world does that add up to 30

2n+2n+2+2n+4=30

 

[DaveC426913]

I interpret
2(3n+3)=30

2n+2n+2+2n+4=30

OK, but we're not solving for what you've called n, we're solving for one of those three sides, which you've defined as 2n.
(the three sides are 2n, 2n+2 and 2n+4).

So if n=4 then the shortest side is 8.

 

[phinds]

Yes.


I'm not sure how you arrived at those other two numbers. His formula doesn't produce 5 and 6.

AH HA !!! Consecutive EVEN integers. Now, if I could only learn to read before opening my mouth.

 

[DaveC426913]

AH HA !!! Consecutive EVEN integers. Now, if I could only learn to read before opening my mouth.

Yeah. That's a real gotcha. Tripped up a lot of peeps.

 

[Gavran]

A triangle has sides that are consecutive even integers.

"sides" in the problem statement can be two sides or three sides.
Between two solutions (14,12,4) and (12,10,8), the first one is correct because 4 is less than 8.

 

[DaveC426913]

"sides" in the problem statement can be two sides or three sides.

Indeed. That's the way I read it, each of the dozen or so times I read it. I just assumed they were only defining the properties of the first two sides. Never occurred to me it could mean all three, let alone that that's probably what they did mean.

Between two solutions (14,12,4) and (12,10,8), the first one is correct because 4 is less than 8.

This does not follow.

The length of short side of the specified triangle could be 8 or 4.

It does not say what is the shortest possible length of the short side, given all valid triangles.

 

[Gavran]

This does not follow.

The length of short side of the specified triangle could be 8 or 4.

It does not say what is the shortest possible length of the short side, given all valid triangles.

It means that both answers are correct.

 

[DaveC426913]

It means that both answers are correct.

Ok, I thought you were saying one was correcter than the other.

 

[anuttarasammyak]

Interpretation of chat GPT is unique:

We are given a triangle with sides that are consecutive even integers, and the perimeter of the triangle is 30 inches. We need to find the length of the short side.
Let the lengths of the sides of the triangle be represented as consecutive even integers. We can define the sides as follows:

• The shortest side: x
• The second side: x+2
• The third side: x+4 Etc.

 

[Mark44]

Let the lengths of the sides of the triangle be represented as consecutive even integers. We can define the sides as follows:

• The shortest side: x
• The second side: x+2
• The third side: x+4 Etc.

Or more simply, emphasizing that all three sides are even integers:
$2n - 2 + 2n + 2n + 2 = 30$
$\Rightarrow 6n = 30 \Rightarrow n = 5$
The three sides are 8, 10, and 12.

Since there was no mention of the triangle being a right triangle, I have assumed that the term "sides" in the problem refers to all three sides. It's only with right triangles that "sides" are distinguished from the hypotenuse.

 

[anuttarasammyak]

I changed the question : A triangle has two or three sides that are consecutive even integers. The perimeter of the triangle is 30 inches. What is the length of the short side? Then Chat GPT answered the two cases.

 

[DaveC426913]

I changed the question : A triangle has two or three sides that are consecutive even integers.

It would be sufficient to say "A triangle has two sides that are consecutive even integers..."

Specifying the third is redundant. You'll still get the same two solutions.