## The triangle answers

##### Fractal Goizane.

1. Answer the following questions:
a. If the area of the triangle is 1m2, what is the area of the greatest square?

The area of the greatest square is 0,5m2 .

b. What is the area of the next square? and the others?

The area of the next square is half of the previous and so on.

c. Repeat this process if the area of the initial triangle is x.

If the area of the initial triangle is x, the area of the greatest square is x/2.
And the areas of the following squares are half the previous square.

d. What is your opinion about the areas? Explain what you see.

What I see is that the area of the square is half the square greater than it. And of the largest square its area is x (area of triangle) /2.

##### Fractal Juan Alexander Lazarov Argilashki

1. Draw a right angled triangle whose legs are equal (Isosceles right angled triangle)
2. Draw one square with the following conditions:
a. One vertex is the apex of the triangle.
b. Its side length is one half of the side of each leg.
3. Repeat this process at least 7 times.
4. Answer the following questions:
a. If the area of the triangle is 1m2, what is the area of the greatest square?
The area of the greatest square is 0’5m2.
b. What is the area of the next square? and the others?
The area of the next square is 0’25m2, and the others is all the time the half of the previous time.
c. Repeat this process if the area of the initial triangle is x
x/2, x/22, x/23, … x/2n
d. What is your opinion about the areas? Explain what you see
If you take the square and chop it in half you can fulfil the empty spaces.

##### Fractal Irene

a. If the area of the triangle is 1 m2, the area of the greatest square is 0´5 m2
b. The area of the next square is 0´25 m2, and the areas of the other squares are the half of its previous square.
c. If the area of the initial triangle is X, the area of the greatest square equals x/2, the next square´s area is equal to x/2^2, the next one equals x/2^3 , the next one is equals to x/2^4 , the next one equals x/2^5 and so on.
d. I believe to calculate these areas or continue calculating new squares´ areas, we only have to calculate the half of the previous square.