Thursday, April 26, 2018

POTW #29 - Upcoming Gauss and Caribou

We will have our last Caribou contest for the year on May 2nd. We will write it in the morning. The interactive game is Sokoban. Don't forget we also have the Gauss contest for those students who had requested. It will be on May 16th and I have lots of practice tests so please ask! (Seayrohn, that' you!).

POTW #29 Question:


POTW #28 Solution:


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6 comments:

  1. Fiona BianMay 2, 2018 at 8:11 AM

    POTW:
    I'm not really sure how to solve this problem, but I'm thinking that it has to do something with the Pythagorean Theorem :
    1. Find the height, find the lengths of the bases. Subtract the top base from the bottom base to the find the "extended" part on the second base. Divide by 2 to get the length of one "extended" part, then use the height, and find the slant with the Pythagorean Theorem.
    This is all I have right now:
    Height: D which is twice the radius. Height= 20 cm
    The two bases would have an average of: (510/20= 25.5)
    and a sum of (25.5 x 2)= 51

    This is where I'm stuck, I'm not sure what each base would be. :)

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    Replies
    1. AnonymousMay 3, 2018 at 6:20 PM

      I got the same first part, however, I found out that the midpoint of each parallel line is equivalent to the diameter of the circle, 20cm. Based on this, each base must be linked to 20cm. 10.5cm and 40.5cm would be fitting approximations based on relations to the midpoint and meeting the sum requirement. The extension on the second base would be 30cm. Divided by 2 would be 15cm. Now, using the Pythagorean theorem you can find that X=25cm.

      Delete
    2. AnonymousMay 3, 2018 at 8:23 PM

      This comment has been removed by the author.

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    3. AnonymousMay 12, 2018 at 8:36 AM

      Same here. I get stuck at that part.

      Delete
  2. AnonymousMay 2, 2018 at 9:02 PM

    Building off of Fiona's comment:

    If the average of the two bases is 25.5, then we already know one base (top) which is 20cm. And the bottom would automatically become 31cm.

    If we know that, 31-20 = 11. 11/2=5.5cm.

    This means that both sides go out 5.5cm.

    Now we can use the Pythagorean theorem.

    5.5^2+20^2=c^2

    30.25 + 400 = c^2

    430.25 = c^2

    c = 20.74cm

    Not sure if this is correct but that is my take on the question.

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  3. AnonymousMay 3, 2018 at 7:50 PM

    This question made almost no sense to me. The circle in the trapezoid seemed to be quite a common question, but I really couldn't think of much of a solution. Thinking more rwa, maybe Pythagorean Theorem could help solve the problem as it is in the curriculum, or maybe using geometry shape formulas. I couldn't fully grasp the whole concept of this question either way.

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