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# just need conformation ;)

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Trisect each side of an equilateral triangle of side length 2 and construct an equilateral triangle on the center third of each side. Omit the side of each new triangle that was once a part of the original triangle. Repeat the trisection, construction, and omission steps on each segment formed above, creating the figure below. When this process is repeated indefinitely, a new figure is approached. The square of the area of this new figure can be written as
where p and q are relatively prime positive integers. Find p + q. ps. the figure is a koch flake. pretty sure the answer is 223, but i some conformation. thank you :)

Jun 27, 2024

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+1075
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I think it's just a glitch but the problem is missing some values.

We need to know that the area of the square can be written as for p and q to solve this problem.

I think the latex didn't go through.

Can you please just fix the part for the equation?

I'll try to solve it then!

Thanks! ::)

Jun 27, 2024
#2
+85
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Trisect each side of an equilateral triangle of side length 2 and construct an equilateral triangle on the center third of each side. Omit the side of each new triangle that was once a part of the original triangle. Repeat the trisection, construction, and omission steps on each segment formed above, creating the figure below. When this process is repeated indefinitely, a new figure is approached. The square of the area of this new figure can be written as p/q
where p and q are relatively prime positive integers. Find p + q. ps. the figure is a koch flake. pretty sure the answer is 223, but i some conformation. thank you :)

this is the edited version. thank u :)

Jul 2, 2024
#3
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This is a tough questipn! It takes some thought to solve! Good one!

Now, let's note something really important first.

The area of the koch flake can be written in the form

where a_0 was the original area and n was the iteration number.

The limit of the area in terms of sidelength s is

Thus, plugging in 2, we have

$$\frac{8\sqrt3}{5}$$

Now, we square it and see what we get. We have

$$\frac{64(3)}{25} = \frac{192}{25}$$

So $$p=192; q=25$$

Thus, $$p+q = 25+192 = 217$$

Hmmm, I'm not sure if I'm correct. Can you explain your thought process. I think I misunderstood my own logic...

I am pretty sure I'm wrong...ummm, is there a way you can check?

Thanks! :)

~NTS

Jul 2, 2024
edited by NotThatSmart  Jul 2, 2024
edited by NotThatSmart  Jul 2, 2024