The Magic Box

A string that is L inches long is cut into two pieces w/ one twice as long as the other. The long piece is used to make a square and the short one is used to make a circle. What is the ratio of the area of the square to the area of the cirlce?

the answer i finally got was .094 : 1/6...

but i'll ttyl! 😄 night!

Originally posted by Jury
Now I think the answer is [b]1:1 🙂 [/B]

Too lazy to edit... sorry but I mean PI:1

Let me show you how I got PI:1

The longer piece must be (2/3)L
and the shorter must be (1/3)L

so that one piece is twice as long as the other.

Making (2/3)L as a square will become (1/4)(2/3)L as one side of the square resulting it into: (1/6)L

The area of the square therefore must be [(1/6)L]^2
which is (1/36)L^2 or (L^2)/36

The other piece will be the circumference of the circle
which is (1/3)L which is also equal to 2PIr
where r = (L/6PI)

The area of the circle therefore must be PI(L/6PI)^2
which is (L^2)/(36PI)

Now the Ratio is (L^2)/36 : (L^2)/(36PI)

will become PI : 1

😐

why am i still up? 😛

well...heres what i did...i did this a long time ago, so on part of it i don't even remember why i did what i did...all i know is that its the right answer....🙂

i used A=PI(r^2) and C=2PIr
so that 2PIr=(1/3L)/2PI
PI x ((1/3L)/(2PI)^2) : (2/3L)/2
then i started reducing (1/9)(L^2)/4PIA : (2/3L)/2
(1/3L)/2(PI^-2) : (2/3L)/2
(1/3)/2(PI^-2) : (2/3)/4
.094 : 1/6

make sense?

alright...i'm really leaving now! 🙂 no more math...must sleep! 😛 night bud! 🙂

wait 😐 i don't get it.. what is (2/3)L/2 by the way?

PI x ((1/3L)/(2PI)^2) : (2/3L)/2

..and I thought we're getting the Ratio of the AREA of the SQUARE to the AREA of the CIRCLE... 😕 and you're doin' otherwise...

oh... i suppose you were sleepin' by now. 😄

I'll make my side clear...

Given two strings:
(2/3)L and (1/3)L

Let's make a square with a perimeter (2/3)L
and figure out it's area.

A= [(1/4)(2/3)L]^2
A= (L^2)/36

Now for the area of circle with circumference (1/3)L

C = 2PIr = (1/3)L
where r = [(1/3)L]/2PI = L/6PI

A = PIr^2
A = PI(L/6PI)^2
A = (L^2)/36PI

and the Ratio we're getting is

Area of SQUARE : Area of CIRCLE

...which is

(L^2)/36 : (L^2)/36PI

or we will have

36PI(L^2) : (L^2)36

and there i got

PI : 1

😐

But I'm not that sure actually 😛

you can correct me in that matter anytime...
see yah next time

😎

Anyways, I have a new problem here:

I called it

The Magic Triangle

Given a triangular object with a square hole in the figure below, and with labels indicated,

(a) Figure out the area of the whole triangle ADE using the formula:

A = (1/2) base x height.

(b) Using the 8 parts of the triangle (not including the hole), figure out the area of each part and sum up all the areas so that it will be the actual area of the given object.

(c) Finally, compare the results of (a) and (b).

Did you get the same results?
If yes, can you explain why the results are the same, in spite of the hole?

😎

And another one:

The Magic Rectangle

Given a rectangle with dimensions 9 x 7 units, it shows that the area is 63 sq. units.

Using the parts and respective measurements indicated,
sum up all the areas of the parts so that you'll get the area of the given rectangle.

Compare your result to the area of the given rectangle.

Did you get the same result?

If not, can you explain why?

😎

Anybody wanna try? 🙄

i can't do it

Originally posted by Mighty Yoda
i can't do it

sorry mate. My brain isn't working. Yoda can't think

no prob, man 😉

OK

So, Lianslo... have you seen my new problems? Care to try them? 🙄