Yet another viral math equation is taking over Twitter, with many users struggling to figure out how to make sense of it.
Ed Southall, author of “Geometry Snacks,” shared a photo of a pink triangle inside of a square and challenged people to figure out how much of the square is shaded pink.
What fraction is shaded? pic.twitter.com/f4kAjoX4C7
— Ed Southall (@solvemymaths) April 23, 2018
Some people gave up immediately.
That pink shaded region is
— Derek Orr (@Derektionary) April 23, 2018
5 out of 4 people struggle with math.
— Papa Santos (@jedimasterpapa) April 27, 2018
Pink is so 2017.
— Vincent Pantal🍩ni (@panlepan) April 23, 2018
But other users rose to the challenge.
Simplest answer I can think of:
– Pink triangle and little triangle have all the same angles: they’re ‘similar’
– Base of pink is twice base of little
– So height of pink is also twice height of little
– So height of pink is 2/3 of whole square
– So area = half x 1 x 2/3 = 1/3 https://t.co/7Hxz3R4VtH
— David Weston (@informed_edu) April 24, 2018
— Hedy Lim (@hedy20lim) April 24, 2018
So height of pink triangle = 2/3 length of square, hence
area(rectangle under black dotted line) = 2/3 area(square)
= 2 area(pink triangle)
The answer is 1/3! pic.twitter.com/GcoWpjFBKK
— Smoky (@SmokyFurby) April 24, 2018
— Baste Atharva (@_Aaru9) April 27, 2018
According to Business Insider’s quant reporter Andy Kiersz, the key to solving the problem is the height of the pink triangle.
The area of a triangle is 1/2 (base x height). If we assume that the square is a 1 x 1 unit, we can see that the base of the pink triangle is 1, the length of the square. All we need to figure out is the height.
“The key trick is that the little triangle up top is similar to the pink triangle, which means that the little triangle is just a smaller version of the pink triangle,” Kiersz said.
“A property of similar triangles is that the ratio of the triangles’ heights will be the same as the ratio of their bases. Since the pink triangle’s base is twice the little triangle’s base, its height is also twice the little triangle’s height. But we know that the little triangle’s height plus the pink triangle’s height is 1, so that means the pink triangle’s height is 2/3. Plug that on in and we get our area = 1/2 x base x height = 1/2 x 1 x 2/3 = 1/3.”
Southall confirmed to INSIDER that the answer is indeed 1/3. Congratulations if you managed to solve it!
This article was originally published by Business Insider.
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