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The Prophet & Moderator
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Re: It can't be true ... can it?


p = 12

legs = 15, 20

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Spikosaur, of the Uncircumcised Umbrella, Prophet to The Collectors, OA, RMC

Hail Apostle Paul
Praise to Founder Bunny
Glory to the Objects
8/23/2018, 9:23 pm Link to this post Send Email to Spikosauropod   Send PM to Spikosauropod
 
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The Prophet & Moderator
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Re: It can't be true ... can it?


This was much easier than the other, although I started off solving it in a much more difficult way than I had to. It can all be solved with ratio and proportion. Once you see that 16/p = p/9 you are basically done.

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Spikosaur, of the Uncircumcised Umbrella, Prophet to The Collectors, OA, RMC

Hail Apostle Paul
Praise to Founder Bunny
Glory to the Objects
8/23/2018, 9:26 pm Link to this post Send Email to Spikosauropod   Send PM to Spikosauropod
 
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Re: It can't be true ... can it?


A square is inscribed in a circle.

A smaller square is drawn. It shares a side with the inscribed square and its other two corners touch the circle.

What is the ratio of the large square's area to the small square's area?


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8/23/2018, 10:05 pm Link to this post Send Email to Exyooper   Send PM to Exyooper
 
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Re: It can't be true ... can it?


That was the hardest one of all.

I got 25.

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Spikosaur, of the Uncircumcised Umbrella, Prophet to The Collectors, OA, RMC

Hail Apostle Paul
Praise to Founder Bunny
Glory to the Objects
8/24/2018, 5:48 am Link to this post Send Email to Spikosauropod   Send PM to Spikosauropod
 
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Re: It can't be true ... can it?


the hard part was finding the size of the small square in terms of r (radius)

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Re: It can't be true ... can it?


A right triangle has a hypotenuse equal to 10 and an altitude to the hypotenuse equal to 6.

What is the area of the triangle?


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Re: It can't be true ... can it?


That one is incredibly easy if you realize that 10 is the base of the triangle and 6 is the height. They actually give it away by calling 6 an "altitude".

The area is 30.

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Spikosaur, of the Uncircumcised Umbrella, Prophet to The Collectors, OA, RMC

Hail Apostle Paul
Praise to Founder Bunny
Glory to the Objects
8/24/2018, 12:30 pm Link to this post Send Email to Spikosauropod   Send PM to Spikosauropod
 
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Re: It can't be true ... can it?


WRONG! This is a trick question. A right triangle with a hypotenuse of 10 can have an altitude (to that hypotenuse) of at most 5.

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8/24/2018, 12:49 pm Link to this post Send Email to Exyooper   Send PM to Exyooper
 
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Re: It can't be true ... can it?


Aha! I was not looking for something like that.

Alas, I am a math teacher, and not an engineer. If an engineer misses something like that, it could be tragic.

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Spikosaur, of the Uncircumcised Umbrella, Prophet to The Collectors, OA, RMC

Hail Apostle Paul
Praise to Founder Bunny
Glory to the Objects
8/24/2018, 1:32 pm Link to this post Send Email to Spikosauropod   Send PM to Spikosauropod
 
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Re: It can't be true ... can it?


Here is a killer problem (with an eloquent solution)

Take an equilateral triangle and pick a random point inside.

Draw from each vertex a line to the random point. Two of the three angles at the random point are known, let's say x and y.

If the 3 line segments from each vertex to the random point were removed out of the original triangle to form a new triangle, what would the new triangle's angles be in terms of x and y?


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