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1. In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points W, X, Y, and Z is a vertex of one of the small squares. Square ABCD can be constructed with sides passing through W, X, Y, and Z. What is the maximum possible distance from A to P?

 

2.  An acute triangle has a side length of  and a side length of  The third side length is also a positive integer. How many different possible values are there for the third side length?

 

3. An obtuse triangle has a side length of  and a side length of  The third side length is also a positive integer. How many different possible values are there for the third side length?

 

thank you :P

 Oct 31, 2020
edited by akacindy  Oct 31, 2020
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1. The maximum distance from A to P is 4 + sqrt(7).

 Oct 31, 2020
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oops! that was wrong!

akacindy  Oct 31, 2020
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If the angle WXA = 22.5º then  AP = 5.991618724

 

I'm not a guest. laugh

 Oct 31, 2020
edited by Guest  Oct 31, 2020
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Please post only one question per post.

 Nov 1, 2020

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