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AD and BC are the two bases of trapezoid ABCD, whose side lengths are labelled in the diagram. The extensions of AB and DC intersect at P. Find the perimeter of triangle PAD.

 

 May 17, 2021
 #1
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Triangles PBC  and  PAD  are similar....so....

 

We  can  find   PC  as

 

PC  / 15   =  (PC + 10) /  27           cross-multiply

 

 

27 PC =  15  ( PC + 10)

 

27PC  = 15PC  +  150

 

27PC -  15PC =   150

 

12PC   =  150

 

PC   = 150  /12   =  12.5

 

And PB  = PC

 

So...perimeter  of   PAD   = 2 (12.5)  + 2 (10)  +  27   =    72

 

 

cool cool cool

 May 18, 2021

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