question to ponder...

[Cosmo]

If u use a 12cm string to form a square n a triangle... wld the areas in both shapes be the same?

 

[ac323]

Re: question to ponder...

If u use a 12cm string to form a square n a triangle... wld the areas in both shapes be the same?

you must be bored???










cheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeers

 

[Red_Bean_Bun]

Re: question to ponder...

Assuming triangle is equilateral ?

Haha!

My daughter would ask .....

 

[Baby1M]

Re: question to ponder...

If u use a 12cm string to form a square n a triangle... wld the areas in both shapes be the same?

1x 12cm string to form 1x square and 1x triangle = the shape will have 6x side, ea side is 2cm. The square is 4cm sq while triangle is half base (0.5*2cm) multiple by height... now u tell me would the area be e same

Promise i didn't search www and hope e above is entertaining enough.

 

[C3P0]

Re: question to ponder...

0012 may be tonight's 4D number. HUAT AH!!

 

[seanskye]

question to ponder...

Very thought-provoking, I had to dig deep into areas of my brain left untouched for decades. The area of the square bound by the 12cm string is 9cm2. Carrying out hypothesis testing of Heron's formula, it is mathematically impossible for a triangle with a perimeter of 12cm to form an area of 9cm2. I put it to the logic test as well using isoperimetric theorem and the maximum area bounded by the 12cm string is approx. 6.9cm2. Again, same answer. Hence, mine is a big NO, unless this is some trick question.

Please thankew me for quality effort yeah! Cheers!!!

 

[casper77]

Re: question to ponder...

Very thought-provoking, I had to dig deep into areas of my brain left untouched for decades. The area of the square bound by the 12cm string is 9cm2. Carrying out hypothesis testing of Heron's formula, it is mathematically impossible for a triangle with a perimeter of 12cm to form an area of 9cm2. I put it to the logic test as well using isoperimetric theorem and the maximum area bounded by the 12cm string is approx. 6.9cm2. Again, same answer. Hence, mine is a big NO, unless this is some trick question.

Please thankew me for quality effort yeah! Cheers!!!

Chim.... so No huh??

Orr...

 

[C3P0]

Re: question to ponder...

Seanskye give me 1292. Thanks bro. If win I will split with u. HUAT AH!!

 

[Baby1M]

Re: question to ponder...

1x 12cm string to form 1x square and 1x triangle = the shape will have 6x side, ea side is 2cm. The square is 4cm sq while triangle is half base (0.5*2cm) multiple by height... now u tell me would the area be e same

Promise i didn't search www and hope e above is entertaining enough.

Adding a picture for clarity...

Alternatively instead of half base multiple by height, we can use (a) half base multiple by Sin A-B-or-C... or (b) 2cm sq multiple square root of 3, then divide by 4... so now u tell me if area of the square and triangle is e same :nehnehhh:

View attachment 59252

 

[LimPeh]

Re: question to ponder...

Adding a picture for clarity...

Alternatively instead of half base multiple by height, we can use (a) half base multiple by Sin A-B-or-C... or (b) 2cm sq multiple square root of 3, then divide by 4... so now u tell me if area of the square and triangle is e same :nehnehhh:

View attachment 59252

Very cheeeem logic. Limpeh catch no ball.
The diagram clearly shows that the area of the triangle is smaller than the square. Right?

 

[Baby1M]

Re: question to ponder...

Very cheeeem logic. Limpeh catch no ball.
The diagram clearly shows that the area of the triangle is smaller than the square. Right?

If based on by TS's original statement below (highlighted bold and red)... where is it 1 single 12cm string forming a square AND a triangle....

If u use a 12cm string to form a square n a triangle... wld the areas in both shapes be the same?

Yups u r right, definitely no equal... thus uploaded graphic to show the obvious.

 

[Red_Bean_Bun]

Re: question to ponder...

But can arrange until both the same if the diagram is like that .....

 

[Baby1M]

Re: question to ponder...

But can arrange until both the same if the diagram is like that .....

Yes, as long as the square has shorter sides. So the question is kind of debunked because there are many variables, I presented 1 where all the 6x 'side' are equal.

 

[LimPeh]

Re: question to ponder...

But can arrange until both the same if the diagram is like that .....

Yah lor. On the same diagram, try a square with each side length of 1.477041cm. A triangle using one side of the square as its base of 1.477041cm and 2 equal sides of length 3.045cm. The area of both square and triangle will be 2.18165cmsquare.

 

[casper77]

Re: question to ponder...

Yah lor. On the same diagram, try a square with each side length of 1.477041cm. A triangle using one side of the square as its base of 1.477041cm and 2 equal sides of length 3.045cm. The area of both square and triangle will be 2.18165cmsquare.

SIbeh chim lay... so simi si simi???

 

[easy]

Re: question to ponder...

If u use a 12cm string to form a square n a triangle... wld the areas in both shapes be the same?

If you are asking is it POSSIBLE for a square and triangle with same perimeter length (12 cm) to to have the same area then the answer is no. One way to understand this is to recall that for a constant perimeter the (plane) shape that maximizes the bounded area is a circle. So I reason that the more the shape departs from "circularness" the less wiill be the area, a square is always more "circular" than a triangle so its area will always be greater.

 

[totoseow]

Re: question to ponder...

I simply cut the string. no strings attached is the best.

 

[kenntona]

Re: question to ponder...

If the question is indeed 1 string = 1 square + 1 triangle to have equal area,

then there are two equations:

(1) square's width times 4 plus two sides of triangle = 12

4w plus 2s = 12

(2) area of square (w times w) = area of triangle (0.5 times w times h)

w square = 1/2 time width times height

Jammed here. How do I link s and h to solve for the 2 equations?