Math Is Fun Forum

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 245

An Unusual Tricky Exercise, Have Fun

The perimeter of a square (Ps) is equal to the perimeter of an equilateral triangle (Pe).

And the area of the square (As) is ‘k’ times equal to the area of the equilateral triangle (Ae), that is As = k*Ae.

Find the right value of ‘k’ in the 5 expressions below:

(1) 6 / [3*sqrt(3)]

(2) 9 / [4*sqrt(3)]

(3) 2*sqrt(3) / 3

(4) 6 / [4*sqrt(3)]

(5) 3*sqrt(3) / 4

As we will see, the way this exercise is stated lets it be tricky to all students but not necessarily to skilled teachers.

Have fun.
Kerim

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: An Unusual Tricky Exercise, Have Fun

The perimeter of a square (Ps) is equal to the perimeter of an equilateral triangle (Pe).

And the area of the square (As) is ‘k’ times equal to the area of the equilateral triangle (Ae), that is As = k*Ae.

Find the...value of ‘k’

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 245

Re: An Unusual Tricky Exercise, Have Fun

Hi amnkb,

Your work is right, and you got k = 9 / [4*sqrt(3)], thank you.

But the question of this specific exercise was: "Find the right value of ‘k’ in the 5 expressions below:"

I am afraid, you didn't specify exactly where you find it in these 5 expressions. You just said k = 9 / [4*sqrt(3)].

Please remember, it is an 'unusual' tricky exercise to all students, but not to skilled teachers.

Have fun.
Kerim

Last edited by KerimF (2023-11-24 19:53:45)

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: An Unusual Tricky Exercise, Have Fun

Bob

ps. Aren't we all still students?

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 245

Re: An Unusual Tricky Exercise, Have Fun

Bob

ps. Aren't we all still students?

Hi Bob,

Yes, we are all still students in life, since learning/discovering has no limit.

But, here, only a teacher may notice that 'k' is given twice in (2) and (5), though presented in different forms.

Following the norm, a student expects here that the right answer is (or has to be) given once on the list. So, when he finds the right answer, he just checks (x) on the expression (2) or (5), the one he got at his last step. But, by doing this, he also says, though without his knowledge, that none of the remaining 4 expressions is equal to the right value of 'k' which is wrong.

Kerim

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: An Unusual Tricky Exercise, Have Fun

so i did it wrong b/c im not a teacher?
huh
twi

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 245

Re: An Unusual Tricky Exercise, Have Fun

so i did it wrong b/c im not a teacher?
huh
twi

But, thanks to your first good work and my reply to you, our friend Bob was able to notice. more easily. the second right answer.
So, I guess, if Bob presented his solution before you did, you will likely be the teacher by noticing the second option as he did.

Anyway, this situation may look like a humble example of the saying:
"But many that are first shall be last; and the last shall be first."
So, as possible, I try always to be the last

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: An Unusual Tricky Exercise, Have Fun

I have to own up here. When I did this I thought (5) was the answer. Then I compared with amnkb and read your comment. So I looked harder and put down both answers in my post.

And how many times did I tell students to read the question carefully? 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 245

Re: An Unusual Tricky Exercise, Have Fun

It is clear, to me in the least, that you both, amnkb and you (Bob), are very good teachers.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.