Today’s puzzle - معماى امروز

IEI

IEI

Administrator
Staff member
#6
Nov 10, 2002
14,508
3,341
#6
Let's say the width of the orange is x
-->> so the area = 4x
Since the area are the same, the area of the yellow, pink, and green is 3*4x = 12x
Now let's say the width of the yellow is z
So the area of those is also zx
Hence zx =12x so z = 12
So the whole width of the square is 4 + 12= 16
Area is 16*16 = 256
There are multiple ways to solve this, i.e
To say the whole area is 20x ;)
 
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S

spinhead

Elite Member
#8
Oct 24, 2002
2,124
201
United States of Amnesia
#8
The side of square equals x=16. Therefore, the Area = x*x = 256

why?

(0) Let x be the side of the square, its area is x*x
(1) Let L be the length of the Orange rectangle
(2) area of the Blue rectangle = x(x-L)
(3) area of the Blue rectangle also equals x*x/5
(4) solving x(x-L)= x*x/5 gives L=4x/5
(5) The area of the Orange rectangle = 4*L
(6) Substituting the expression obtained in step (4) makes the area of the Orange rectangle = 16x/5
(7) area of the Orange rectangle also equal x*x/5
(8) Solving 16x/5 = x*x/5 gives x=16
 
Last edited:
Likes: IEI
S

spinhead

Elite Member
#9
Oct 24, 2002
2,124
201
United States of Amnesia
#9
Iran-Esteghlal-Inter said:
Let's say the width of the orange is x
-->> so the area = 4x
Since the area are the same, the area of the yellow, pink, and green is 3*4x = 12x
Now let's say the width of the yellow is z
So the area of those is also zx
Hence zx =12x so z = 12
So the whole width of the square is 4 + 12= 16
Area is 16*16 = 256
There are multiple ways to solve this, i.e
To say the whole area is 20x ;)
Click to expand...
Very good. It's interesting that your solution is more geometric and mine is more algebraic.
 
Likes: IEI
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