Melody

Please do not post your AOPS questions here. 

Thanks for explaining CV

I wish there was a way we could do this easily without adding the questions to our watch list.

Sometimes I take a pic of the question with Gyazo (which i use for all my pictures)

The metadata is added automatically so I can hyperlink back to the question later on.

Yes   

Thanks Catmg  

Attn: Helpplzplzplz:

This is a very standard problem that could have come from anywhere.

Please do not spend your time dobbing on other question askers. 

It really is not a good look.

Good spotting EP   

Well, I drew the pic, and it does, on my graph anyway  (I replaced P with A' )

Also answered here

just use Pythagoras's theorem to work it out.  The Pythagorean triple that they gave you is irrelevant.

Hint:

Since you want the shortest side, there will be a take away.  (minus)

Recall that a perfect square is the square of some integer. How many perfect squares less than 1,000 can be represented as the difference of two consecutive perfect squares?

so... how many Pythagorean triads are there such that the smallest one squared is less than 1000

Pythagorean triads with a prime number

sqrt(1000) = 31.6227766016837933

I get 16 but there is probably a much better way to do it.

AND

I need to see how you attempt my teaching questions that I have asked you.

It is no wonder you cannot learn if you do not even attempt to follow your teacher's (my) instructions.