1 small Geometry problem: find length of side DP

[DanteQ]

I had to make a whole list of geometry problems, and could solve them all, except the last one. I need to find the length of side DP. I have no idea how to handle this one...

Sorry for the bad quality pic, but my scanner is having some problems...

 

[Loren]

Re: 1 small Geometry problem

What other information is given besides the drawing?

 

[TchrWill]

I had to make a whole list of geometry problems, and could solve them all, except the last one. I need to find the length of side DP. I have no idea how to handle this one...

Sorry for the bad quality pic, but my scanner is having some problems...

1-Let the altitude from P to E on AD be a.
2-Let the altitude from P to F on BC be b.
3-Let DE = CF = x
4-Let AD = BC = L
5-x^2 + b^2 = 25
6-(L - x)^2 + b^2 = 49
7-(L - x)^2 + a^2 = 36
8-a^2 + x^1 = N^2 = (PD)^2
9-25 - x^2 = 49 - (L - x)^2
10-36 - (L - x)^2 = N^2 - x^2
11-49 - 25 + x^2 = 36 - N^2 + x^2
12-24 - x^2 = 36 + N^2 + x^2
13-24 = 36 - N^2
14-N^2 = 12
15-N = PD = 2(sqrt3)

 

[Denis]

OK Dante, show us what you learned:
CP = 52, BP = 60, AP = 39 ; DP = ?