Solve this in your head!

#math #geometry #puzzle

Improve your critical thinking skills through mathematics and logic puzzle. My channel mainly discuss about mathematics/geometry puzzles, and sometimes can be logic puzzles.

In this mathematics/geometry puzzle, we have 3 squares with area 4, 9, and 36, what is the formed triangle's area? we do not need Pythagoras for this one.

keywords: math, geometry, geometric, catriona agg, many geometric puzzle videos are inspired Catriona Agg, and Mirangu.

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Creative Commons CC BY-SA 3.0
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[tanmoymisra]

This channel needs more attention.
Its way too good content for so measly views.
Keep up the good work man👍👍.

[monroeclewis]

I added the areas of all the similar triangles to the areas of the squares to get 75. The top orange triangle is composed of 2 smaller triangles, one on the left side, one on the right, each one similar to the smaller triangles on its side of the large triangle, left and right.

[Константин-лкэ]

at 2:00 you went difficult way. it is clear for the top tri (based on tangences we have seen from aside tris) that 0, 5 x + x = 6, i.e x=4, therefore h=10, area=75

[cubetoast]

We can also solve it by drawing a perpendicular to the 6cm side of the top triangle.

[Awesome-]

We define the side of the triangle on the right to origin from point (0, 0)

We have this point passing through the corners of both the 4, 36 squares.

There for we get another triangle with base of 2 and height of 4.
Divide 4 by 2 and we get that the slope of the hyppotenuse is 2.

We also said its origin is 0, 0 so we will define it as y=2x

We have the side of the 4 square which is 2 so we plug y=2 in our equation
And we get 2x=2, x=1.
Since its perpendicular to the x axis
So the distance from the origin to the 1st square is 1 unit.

Now we look the other side.
We have the same idea.
Triangle with sides 3 and 3
In a negative slope. We get that m=-1.
If we count all bases we get and a side of the 9 area square which is 3.
We get the point (12, 3)
Now we can assemble another line.
y-3=-x+12 ---> y=-x+15.

Now the 2 line we found intersect at a point which its y will serve as the height of the triangle.
2x=-x+15
3x=15 ---> x=5
y=2×5 = 10 and we get height of 10.
The base will be the x of intersection point with x axis.
0=-x+15 ---> x=15 and we get base of 15.

S=15×10×1/2 = 75

[CugnoBrasso]

Nice, your method was smarter than mine. I used analytic geometry to find the equations of the lines, which were y = 2x and y = -x + 15, then I basically did the integral.

[erikschmidt]

Very cool. I had basically the same approach, but how are you supposed to do all that in your head??