Maths Puzzle

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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 '?'

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: 4 • Views: 6,725 • Replies: 20
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https://i.pinimg.com/originals/fb/8a/dd/fb8add2877b48f6158397a3112806ba7.jpg

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@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.

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Are there no mathematicians about ?

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@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.

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@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?

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@engineer,

Just the numeric area of the green part alone in square units.

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No constructive comments to this similar triangles riddle yet.
I reckon the answer I have will inspire more enthusiasm.

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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.

1 Reply

@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.

1 Reply

@engineer,

For the benefit of our members, would you kindly explain your reason for the
white area being 9/2.

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@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.

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@Beaker17,

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.

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@engineer,

Thank you so much. That is an excellent and educational reply and should be of great benefit to readers.

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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.

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@engineer,

Dude... All this time time I thought "engineer" was for like trains...

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@Beaker17,

A = 19.56 Finding the lengths and widths is a matter of congruence. Estimations are a must (like with IQ tests) and vary the established answer based on preference of method. The length of the rectangle is equal to the height x2 + 2/3xh + 1/9 of 2/3h. From there its a matter of mathematics. I was a drinking while I did the math so I kept it simple.

1 Reply

@Osibos,

Osibos wrote:

A = 19.56 Finding the lengths and widths is a matter of congruence. Estimations are a must (like with IQ tests) and vary the established answer based on preference of method. The length of the rectangle is equal to the height x2 + 2/3xh + 1/9 of 2/3h. From there its a matter of mathematics. I was a drinking while I did the math so I kept it simple.

Because of the long numbers I encountered during the process of equating it, I assume that this is likely a side view of a pillar slice. The way it seems to slip away from you and back around the other side, similarly the way the numbers go on in either direction. No matter how you calculate it. I lacked a ruler so I fashioned a piece of paper instead.

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@Osibos,

Quote:

Because of the long numbers I encountered during the process of equating it, I assume that this is likely a side view of a pillar slice. The way it seems to slip away from you and back around the other side, similarly the way the numbers go on in either direction. No matter how you calculate it. I lacked a ruler so I fashioned a piece of paper instead.

Welcome to able2know.org

Stunning analysis.

Excellent posts and questions.

Keep the piece of paper.

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@nacredambition,

Came back sober: A = 16.2005626, because of inexaction I have reason to believe that the areas "2" and "3" are actually wrong, and too simple. Although it may hint that the equation is supposed to be simplified, so the answer would then be 16. Same reasoning as above. I may have accidentally simplified one number during the process but I can't find it in the relative formula I used. Hehe, I think I know what this is about.

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Maths Puzzle

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