This was asked in a Chinese Grade 5 exam! 🤯 Parallelogram and Triangles Problem - Math Olympiad Prep

This beautiful problem uses the simple geometry result:
"Area of the triangle is half the area of the parallelogram with the same base and height."
Apparently it was asked in one of the Chinese exams meant of 5th grade gifted students.
Question Credits: / @mindyourdecisions
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[@yashwant12-b50]

Brother keep it up. We need more of them

[@BlunderMunchkin]

A nice, practical problem with obvious applications in day-to-day life.

[@SRAVANAM_KEERTHANAM_SMARANAM]

Most of the followers of your channel i believe would be children. you are any how getting diversified into many areas. Kindly also consider putting some inspirational short stories for children so that they get inspired to learn.

[@saltybaguette7683]

I don't understand how your solution works, I got to the same answer by producing a system of linear equations derived from the same principes (but instead of triangles = 1/2 area of parallelogram , the triangles are equal to the remaining triangle, same thing)
But how can you make the assumption those m and n are the same value? They may be, but it was never established

[@m3cubee]

can you please explain your question? I can't understand

[@saltybaguette7683]

@@m3cubee Here's what I did:
First I assigned each small section starting from the top left a variable name for their area: a, b, c, d...
I also assigned each large triangle spanning the length/width of the parallelogram a variable name: A, B, C...
Notice there are two sets of triangles, the vertical triangles, and the horizontal triangle.
There are 3 horizontal triangles: A, B, C. A and C point left, B points right.
Do the same thing with the 4 vertical triangles: D, E, F, G D and F point down, E and G point right.
Each triangle area can be described by it's subsections: A = a + b + c + d, D = a + e ...
B and D in this case are the same triangles cuemath uses in their video to find ?, which is a in my example.
As stated in the video, a triangle like B, takes up 1/2 of the parallelogram's area. Therefore A+C make up the remaining half. If we do this for both the vertical triangles and horizontal triangles we get:
B = A + C meaning: 0 = 1A + (-1) B + 1C + 0 D + 0E + 0 F + 0G (Call this F1)
D + F = E + G meaning: 0 = 0A + 0 B + 0C + (-1)D + 1E + (-1)F + 1G (Call this F2)
This is that system of linear equations I was talking about.
By substituting the triangle variables by their sub component variables: ie A = a+b+c+d, we get a system of two functions like above, but that are comprised of a,b,c,d,e,f,g,h,i,j
We can then add them together such that we are left with a function (F3) similar to:
0 = 2a + 2c - 2f - 2h + 2j
Since c =72, f=79, h=10, j=8. Solve for a, you'll find a = 9
What I don't understand is how the video claims we're able to go from these triangles sum up to a half of the total area, to these specific sub components are equal. In my example, this is as if I told you out of the blue that the subsections: b=g and d=e. But at no point did the youtube video prove that (as far as I can tell)
I hope you're able to make sense of my comment!

[@arandomdude9629]

​@saltybaguette7683 But he does not say that m = n? It's just that (m + n) appears in both equations so when equating, you can cancel them out.

[@saltybaguette7683]

@@arandomdude9629 Thank you for the tip, I see it now. Same concept but so much simpler than my solution XD

[@tejasinternationalschool-cu9fz]

Thanks for 0 likes 😢❤

[@sade9709]

Respected Sir,
Your official email id or whatsapp number please. I have an issue about age calculator on your website.