Thursday, 17 May 2012

IQ test [Updated, May 2012]


By Jackie, Researcher
Area of discussion: Intelligence Quotient [IQ]
Function of this discussion: To test our brain’s IQ
Requirement(s): Basic Mathematics’ skills involving area calculations

The objective of this post is to share an extremely tricky question related to IQ and see whether could we solve this question together. Besides, it allows us to share the conflicts or perhaps some weaknesses in Mathematics’ theories. By having different comments and opinions from different people will greatly help to solve this problem faster.

Introduction
Guest what? I saw this on my Facebook, and yet no one can give an accurate or reasonable explanation on why this could happen. So, I took this opportunity to share out to a larger crowd to see whether it could be solved or not?


My arguments:

I know there is a difference of 1 unit² between the first triangle and the second triangle, but I am going to tackle them separately as the confusion already exist if we tackle either one of them even without the existence of the other triangle.

(The triangle at the top)

According to Mathematics’ theory:
Area of a triangle 
= 0.5(length x height)
= 0.5(13x5)
= 32.5 units²

But this is different if we calculate it one-by-one, all the four shapes together:
Red: 0.5(8x3) = 12 units²
Orange: 7 units²
Dark green: 0.5(5x2) = 5 units²
Light green: 8 units²
Total : 32 units²

Why is there a difference of 0.5 unit² exist?

(The triangle at the bottom)

According to Mathematics’ theory:
Area of a triangle 
= 0.5(length x height) – 1                                                                      (note: minus one for the missing unit)
= 0.5(13x5) – 1
= 31.5 units²

But this is different if we calculate it one-by-one, all the four shapes together:
Red: 0.5(8x3) = 12 units²
Orange: 7 units²
Dark green: 0.5(5x2) = 5 units²
Light green: 8 units²
Total : 32 units²

Again, why is there a difference of 0.5 unit² exist?

I know some of you may argue that one of the triangles is concave, and the other is convex (or perhaps the triangles are bend at the hypotenuse, but this is not important anymore if we treat them as a separate IQ question. This is because the difference in calculation of 0.5 unit² already arises even if we did not compare the first triangle at the top with the other triangle at the bottom. Therefore, is the calculation wrong? Or is there a conflict between calculating one-by-one method and calculating by using Mathematics’ formula related to triangle?


8 comments:

  1. The calculation is definitely wrong. Without even comparing the two triangles, it is still visible that the "triangle" shown on top is not a triangle. Hence, calculating its surface using formula for calculating the triangle is wrong.

    First, allows me to define what this triangle, using standard polygon. A triangle is a polygon with 3 straight sides, and 3 angles. The diagram above have 4 straight sides when placed together, thus creating 4 angles; 3 acute, 1 reflex. This in turns, means that the shape does not falls under triangle.

    Second, we can calculate that even from the first shape that there will be 0.5 units difference. One way of doing this is to treat it as a regular triangle, and double it to get a rectangle. It can be illustrated in the calculation below.

    Supposed area of rectangle created by two "triangles" shown in first figure
    = 13 x 5 units
    = 65 units

    Actual area covered by "rectangle" created by first diagram
    = 2(0.5(2 x 5) + 0.5(3 x 8) + (7) + (8))
    = 64 units

    Since, as mentioned in the first point, this figure is not a triangle, thus it is unable to be completed into a whole rectangle by doubling the shapes used in constructing the first figure.

    ReplyDelete
    Replies
    1. Oh, I get it... problem solved, thank you very much... Chris Chai = Chai Chan Hoong? We lose contact after Form 3... 7 years already... Where are you now? Come add me on facebook... jackiechanhoileong@yahoo.com or give me your email, i will add you...

      Delete
    2. Yeap, I go by that name now. Easier for people to remember. :)

      Delete
  2. This comment has been removed by the author.

    ReplyDelete
  3. Hi, Nice post! Would you please consider adding a link to my website on your page. Please email me back.

    Thanks!

    Harry
    harry.roger10@gmail.com

    ReplyDelete
    Replies
    1. Give me your url. Is it this one: http://ithinkaboutmoneyallday.blogspot.com/ ?

      Delete
  4. wow... your blog is cool Jackie.. keep posting, followback success #121 (Funny)

    ReplyDelete