Area of an Equilateral Triangle

[Madalch]

Well the teacher who administered the test said they knew about the error. I didn't get a good explanation why they asked a question with no correct answer in the choices given. She was "tickled" that a parent was involved enough to question the test. Sorta sad that I was the only one.

Why do I get the feeling that the other parents looked at it, threw up their hands, and said, "I don't know. I've never needed to find the area of a triangle in real life, so it doesn't matter. You just ignore your math from now on and focus on things that are important- like football."

 

[TjW]

Well the teacher who administered the test said they knew about the error. I didn't get a good explanation why they asked a question with no correct answer in the choices given. She was "tickled" that a parent was involved enough to question the test. Sorta sad that I was the only one.

Tell her that's the wrong answer.

 

[JoeTheJuggler]

Looks very much like a question setter error, ie the setter thinks an equilateral triangle with a perimeter of 15 inches has equal sides of 5 inches (true) and splitting the triangle in two to ease calculating the area produces another side, also of 5 inches (not so true).

Therefore I suspect the correct answer is 12.5.

Yep.. I think that's what the question writer was thinking.

I'd add though that technically speaking that answer is correct if the instructions said something like "choose the best answer from the given choices" as is usually the case.

 

[aofl]

Tell her that's the wrong answer.

And she needs to go ask her parents why.

A

 

[commandlinegamer]

Perhaps it was an oblique way of showing children that those in authority don't always know what they're talking about.

 

[Mason]

Instead of halving the triangle into two right triangles, I imagined it as one sixth of a hexagon, which is pretty close to a circle, so I estimated the area of the circle it would fit in. Given a diameter of 10, and rounding pie to 3, 375 ml of chianti, and divide by six.

Anwser: d.

 

[psionl0]

Instead of halving the triangle into two right triangles, I imagined it as one sixth of a hexagon, which is pretty close to a circle, so I estimated the area of the circle it would fit in. Given a diameter of 10, and rounding pie to 3, 375 ml of chianti, and divide by six.

Anwser: d.

I doubt you could do the last step after 3,375 ml of chianti.
Even if you could, which "d" would you choose?

 

[JoeTheJuggler]

Instead of halving the triangle into two right triangles, I imagined it as one sixth of a hexagon, which is pretty close to a circle, so I estimated the area of the circle it would fit in. Given a diameter of 10, and rounding pie to 3, 375 ml of chianti, and divide by six.

Anwser: d.

In a weird way, that's similar to the point I made earlier.

While I think it's most likely the question was just an error on the part of the test makers, it could have been intentional. Strictly speaking, the closest choice to the correct answer is the correct answer (at least this is given in the instructions of most multiple choice standardized tests).

It's a least possible that the Math Team placement test makers intentionally did this to see what happens when the student calculates a correct answer, but that answer isn't among the choices offered. If it's a timed test, how long the student spends considering what to do might be an inverse measure of self confidence (and perhaps the ability to read and understand the fine print of the test instructions).

There's also the fairly trivial extra step of calculating that d is closer to the correct answer than b, even though the correct answer is between those two choices.

It's certainly something you can do with a multiple choice test that you can't if you just ask students to solve the problems.

 

[sir drinks-a-lot]

I also got 10.8253175473, and agree that the question is wrong.

However, I disagree with the others who think that the wright wrong answer was supposed to be 12.5. I think that is definitely the wrong wrong answer. The right wrong answer is most likely 25, according to the following right wrong reasoning:

1) The base of the triangle is 5
2) The height of the triangle is 5
3) you can therefore chop the triangle in half into two right triangles and rearrange them to make a 5x5 square
4) the area of the 5x5 square would be the same as the area of the triangle, 25

If you are using the wrong wrong reasoning, you'll get the wrong wrong answer.

 

[DuvalHMFIC]

Your kid should have simply answered, "Did you see this triangle, WERE YOU THERE?"

 

[Finster]

Or the teacher erroneously thought that an equilateral triangle would also be a right triangle.

A right triangle with two equal legs of 5 and 5 would have an area of 12.5

 

[CynicalSkeptic]

3) you can therefore chop the triangle in half into two right triangles and rearrange them to make a 5x5 square.

Please explain how you can do this.

 

[SumDood]

At the end of the year competition, I talked to a friend who has been coaching another team for a while. Apparently this question was on last years competition and there were issues then as well. I overheard another coach saying something like 'draw a square around the triangle and figure it out from that' which would imply to use 5 as the height. Then the 'correct' answer would end up being 12.5. Still awful in my book.

The competition was pretty intense. It was about 16 schools from around the area, approximately 200 kids from 4th and 5th grades. Everyone on each team takes a written exam first, which took about an hour. The coaches take it at the same time to check for possible bad questions (and to know if they prepared their team well). Then there was the ciphering portion. The top 5 kids from each team are on the ciphering team. One kid from each school goes up to the front of the auditorium and solves 4 problems, one at a time. They put the problem up on a screen so everyone can see it. They get 3 points for answering the question in 30 seconds or less, 2 for 30-60 seconds and 1 point for answering it in 90 seconds. The only question remember offhand was something like "3300 mm + 2200 cm + 1100 dm = how many meters?" My son's ciphering team came in first and the team came in third overall. Which seems fishy to me since they won the ciphering by a wide margin. My son tied for 5th overall and we cannot be prouder.

 

[sir drinks-a-lot]

Please explain how you can do this.

draw a line from the center of one of the sides and perpendicular to that side to the opposite and use this line to cut the triangle into two right triangles. THen, since it is an equilateral triangle, we know the hypotenuse of each of the right triangles will be the same length. So, rotate one of them by 90 degrees and make the hypotenuses the same line.

 

[sir drinks-a-lot]

At the end of the year competition, I talked to a friend who has been coaching another team for a while. Apparently this question was on last years competition and there were issues then as well. I overheard another coach saying something like 'draw a square around the triangle and figure it out from that' which would imply to use 5 as the height. Then the 'correct' answer would end up being 12.5. Still awful in my book.

Then the 'correct' answer would end up being 25, no?

Interesting that they supposedly knew there was no right answer in the choices presented. Seems fishy to me...

 

[brodski]

I doubt you could do the last step after 3,375 ml of chianti.

Less than 4ml of chianti isn't going to have much effect on anyone.

 

[CynicalSkeptic]

draw a line from the center of one of the sides and perpendicular to that side to the opposite and use this line to cut the triangle into two right triangles. THen, since it is an equilateral triangle, we know the hypotenuse of each of the right triangles will be the same length. So, rotate one of them by 90 degrees and make the hypotenuses the same line.

Right, but that doesn't give you a 5x5 square.

I could see someone mistaking this for a 2.5 x 2.5 square, but of course, it's really a rectangle that is 2.5 x sqrt(25-6.25)

 

[sir drinks-a-lot]

Right, but that doesn't give you a 5x5 square.

I could see someone mistaking this for a 2.5 x 2.5 square, but of course, it's really a rectangle that is 2.5 x sqrt(25-6.25)

Gotcha. I forgot that my method would be dividing the base side in half, so it would be 2.5 instead of 5. And, of course, you're right about the hypotenuse. I knew that part was wrong, but thought it may have been the mistaken notion represented by the test question.

 

[shuttlt]

<late to the party>

 

[sir drinks-a-lot]

<late to the party>

And what a party it is!