Welcome to this new episode of Mr Brain's Puzzle.
Today I propose you a geometry problem.
What is the area of the green square?
Knowing that the area of the yellow square is 60 square meters and the area of the cyanl square is 100 square meters.
The possible answers are sixteen, twenty, twenty-four, twenty-eight square meters.
Pause the video if you'd like to give this problem a try and when you are ready keep watching to learn ho to solve this problem.
Have you found the solution?
Write it in the comments.
Now I will show you a way to solve this problem.
First we find the side of the yellow square.
Let's call the side of the yellow square X.
X is equal to the square root of the area of the yellow square.
The side length of the yellow square is 8
Let's call the side of the yellow square Y.
Y is equal to the square root of the area of the cyan square.
The side length of the cyan square is 10.
Let's color the right triangle located between the yellow square and the cyan square red.
We denote by X the smaller side of the right-angled triangle.
We will use the Pythagorean theorem to find X.
The base of the red right triangle is 6 meters long.
We draw the orange triangle whose base is 8 meter long and is the extension of the side of the yellow square.
The other side of the orange triangle corresponds with the side of the Cyan square.
We want to prove that the orange triangle is congruent with the red triangle.
In other words.
We want to prove that the two triangles have the same side length.
Let's indicate the angles as Alpha, beta and gamma as in the figure
Since Alpha plus gamma equals 90 degrees and Beta plus gamma equals 90 degrees.
It is deduced that alpha is equal to beta.
The yellow and the orane triangle are congruent given the two pairs of corresponding sides and the corresponding angles between them are equal.
At this point we can calculate the area of the green triangle.
The area is found by multiplying the base by the height and dividing by two.
The base is 8 meters long and the height is 6 meters long.
So the area of the green triangle is.....
What a fun logic puzzle!
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See you next episode of Mr Brain's puzzle where we solve the world's problems one video at a time.
4 окт 2024
