3
   

Maths Puzzle

 
 
Reply Mon 9 Sep, 2019 09:34 am
The figure shown in the image consists of a rectangle and the numbers labelled over the top represent the area of that particular shaded region. Calculate the area of the green region labelled as '?'

https://i.imgur.com/Vvf0eky.jpg
It is very hard, some say impossible, but I do have a solution (not mine) which I will post when sufficient enthusiasts have resorted to head banging in desperation.
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Type: Discussion • Score: 3 • Views: 340 • Replies: 15
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knaivete
 
  1  
Reply Mon 9 Sep, 2019 08:36 pm
@Beaker17,
Welcome Beaker.

Two of those triangles look awfully familiar, and you know what the gossip is about the ratio of their areas given the similarity.

Good puzzle , keep 'em coming.
0 Replies
 
Beaker17
 
  1  
Reply Tue 10 Sep, 2019 05:03 am
Are there no mathematicians about ?
tsarstepan
 
  2  
Reply Tue 10 Sep, 2019 06:49 am
@Beaker17,
Beaker17 wrote:

Are there no mathematicians about ?

They all died in the great 8 alarm fire at the Mathematician Warehouse District last Friday. Surprised, you didn't hear about it in the news.
0 Replies
 
engineer
 
  2  
Reply Tue 10 Sep, 2019 06:53 am
@Beaker17,
It seems like the problem is under specified and I'm not sure what type of answer you want. Do you want the green area as a function of the areas of 2 and 3?
Beaker17
 
  1  
Reply Tue 10 Sep, 2019 07:32 am
@engineer,
Just the numeric area of the green part alone in square units.
0 Replies
 
Beaker17
 
  1  
Reply Tue 10 Sep, 2019 09:24 am
No constructive comments to this similar triangles riddle yet.
I reckon the answer I have will inspire more enthusiasm.
Beaker17
 
  1  
Reply Tue 10 Sep, 2019 01:55 pm
It is rather disappointing and somewhat surprising that on a Maths Forum, nobody has taken part in this tricky mathematical problem.
I would have expected some serious mathematical enthusiasts in over 120 views. I myself spent a lot of time trying to solve it when first seen.
engineer
 
  1  
Reply Tue 10 Sep, 2019 02:23 pm
@Beaker17,
I misunderstood your question. I thought the 2 and 3 in the drawing were labels, but I think you meant they are the areas. If that is the case, the white area is 9/2. The green area is (4.5 + 3)-2 = 5.5.
Beaker17
 
  1  
Reply Tue 10 Sep, 2019 05:13 pm
@engineer,
For the benefit of our members, would you kindly explain your reason for the
white area being 9/2.
0 Replies
 
knaivete
 
  1  
Reply Tue 10 Sep, 2019 08:19 pm
@Beaker17,
Quote:
No constructive comments to this similar triangles riddle yet.


"Two of those triangles look awfully familiar, and you know what the gossip is about the ratio of their areas given the similarity".

Oh, I don't know, I thought that this early comment was constructive.
0 Replies
 
engineer
 
  2  
Reply Wed 11 Sep, 2019 07:16 am
@Beaker17,
https://i.imgur.com/Vvf0eky.jpg

If you define the height of the box as H and the length as L, you can also define a position C where the red triangle intersects the long side in the picture. Using H, L and C, you can define the intersection of the two lines and then find the areas of each triangle as a function of H, L and C. When you do that, you find that the area of the blue triangle divided by the area of the red triangle is L/C.

The white triangle and the red triangle are similar, so the area of the white triangle divided by the area of the red triangle is (L/C)^2. You are given the blue and red areas, so you know L/C = 3/2. This makes the white area 2 x (3/2)^2 = 9/2.
Beaker17
 
  1  
Reply Wed 11 Sep, 2019 07:27 am
@engineer,
Thank you so much. That is an excellent and educational reply and should be of great benefit to readers.
0 Replies
 
Beaker17
 
  1  
Reply Wed 11 Sep, 2019 08:43 am
I have entered this puzzle on several Forums, had many hundreds of views and
not a single correct answer. Almost all the replies including those from degree
holders have stated that the information is insufficient for solution.
I have only ever seen TWO correct answers on the web, one of which I show in my image.

The answer given by ENGINEER is nothing short of brilliant and infinitely more simpler and logical
than the rather complex trigonometrical answer I show.

I apologise for the poor quality of my image, it was the best I could get.
Using zoom and adequate concentration, one can just about follow the logic albeit
with difficulty.

Area of green segment = 5.5.

https://i.imgur.com/GH7H3Sy.jpg
0 Replies
 
McGentrix
 
  1  
Reply Wed 11 Sep, 2019 09:15 am
@engineer,
Dude... All this time time I thought "engineer" was for like trains...
0 Replies
 
 

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