question to ponder...
- Thread starter Cosmo
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Red_Bean_Bun
Well-Known Member
Re: question to ponder...
Assuming triangle is equilateral ?
Haha!
My daughter would ask .....
Assuming triangle is equilateral ?
Haha!
My daughter would ask .....
Baby1M
Well-Known Member
Re: question to ponder...
Promise i didn't search www and hope e above is entertaining enough.
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 sameCosmo;1067868 said:
Promise i didn't search www and hope e above is entertaining enough.
seanskye
Well-Known Member
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!!!
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!!!
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Baby1M
Well-Known Member
Re: question to ponder...
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
Adding a picture for clarity...Baby1M;1067873 said: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.
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
Last edited by a moderator:
Baby1M
Well-Known Member
Re: question to ponder...
Yups u r right, definitely no equal... thus uploaded graphic to show the obvious.
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....LimPeh;1067966 said:
Cosmo;1067868 said:
Yups u r right, definitely no equal... thus uploaded graphic to show the obvious.
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Red_Bean_Bun
Well-Known Member
Re: question to ponder...
But can arrange until both the same if the diagram is like that .....
But can arrange until both the same if the diagram is like that .....
LimPeh
Well-Known Member
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.
Red_Bean_Bun;1067969 said:
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.
easy
Well-Known Member
Re: question to ponder...
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.
Cosmo;1067868 said:
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.
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?
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?
