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I think the two other points should be point H and V (the thing is, I don't really get the outside of the square part, but did solve it with a creative method ;D) If I start at P, and need to make 3 equal parts, I know if I look at point P as an angle (so angle RPM), it's 90 degrees. If I want 3 equal parts, it's 30 degrees per section. I know from P to Q, it's 45 degrees (the bisect of the angle, 90), and from Q to M or Q to R, there are 6 other points. Looking at Q to M, I know that 45 is a multiple of 15, so I counted from 0 as M, and K as 15, because there are 6 points, and 45 is made from 15x3, and 3 is half of 6, so I counted by 2. If K was 15, H would be 30 degrees, so my guess is that angle HPM is 30. All I had to do was repeat that with line segment QR. If H was 2 points away from Q, and that made 30 degrees, I can just repeat that. From Q, 2 points away would be V, so I think that angle VPR should be 30 degrees as well, leaving angle VPH to be 30 degrees as well. 30 30 and 30 are all equal, and the flaw in my answer may be that the area is the same, but they're not congruent, so I don't know if this actually answers the question hehehe. But this is what I got!
I like how Emily thinks~ =) I'd have used 'area' as the basis of my solution though... looking forward to seeing what other creative solutions are out there~
Hello. My brother and I answered this question together.
The points we chose were H and V. We knew that the total area of the square was 36m² (6m x 6m) and since it had to be three equal parts, we divided 36 by 3 (36/3 = 12m²). We assumed that two of the three sections would be a triangle and the other an irregular shape.
To find the dimensions of the triangle, we knew that when multiplied it would have to equal to 24 (since the formula of a triangle would be (N x N) / 2 = 12m²).
After some trial and error, we came to the conclusion that the dimensions would be 6 x 4 (28/2 = 12m²) for both triangles. From this, we picked the points H and V.
I think the two other points should be point H and V
ReplyDelete(the thing is, I don't really get the outside of the square part, but did solve it with a creative method ;D)
If I start at P, and need to make 3 equal parts, I know if I look at point P as an angle (so angle RPM), it's 90 degrees.
If I want 3 equal parts, it's 30 degrees per section.
I know from P to Q, it's 45 degrees (the bisect of the angle, 90), and from Q to M or Q to R, there are 6 other points.
Looking at Q to M, I know that 45 is a multiple of 15, so I counted from 0 as M, and K as 15, because there are 6 points, and 45 is made from 15x3, and 3 is half of 6, so I counted by 2.
If K was 15, H would be 30 degrees, so my guess is that angle HPM is 30.
All I had to do was repeat that with line segment QR. If H was 2 points away from Q, and that made 30 degrees, I can just repeat that. From Q, 2 points away would be V, so I think that angle VPR should be 30 degrees as well, leaving angle VPH to be 30 degrees as well. 30 30 and 30 are all equal, and the flaw in my answer may be that the area is the same, but they're not congruent, so I don't know if this actually answers the question hehehe.
But this is what I got!
interesting method!=)
DeleteI like how Emily thinks~ =)
ReplyDeleteI'd have used 'area' as the basis of my solution though... looking forward to seeing what other creative solutions are out there~
Hello. My brother and I answered this question together.
ReplyDeleteThe points we chose were H and V. We knew that the total area of the square was 36m² (6m x 6m) and since it had to be three equal parts, we divided 36 by 3 (36/3 = 12m²). We assumed that two of the three sections would be a triangle and the other an irregular shape.
To find the dimensions of the triangle, we knew that when multiplied it would have to equal to 24 (since the formula of a triangle would be (N x N) / 2 = 12m²).
After some trial and error, we came to the conclusion that the dimensions would be 6 x 4 (28/2 = 12m²) for both triangles. From this, we picked the points H and V.
- Rachel and Jonathan
Way to go! You all obtained the correct answer of points H and V. The best part is you solved it in different ways!
ReplyDelete