Question

Given: P∈ BC , Pabc = 45, Pabp = 30, Papc = 35. Find AP.

Answer 1

10

Explanation:

Pabp = AB +BP +AP

Papc = AP +PC +CA

So the sum of perimeters of the two smaller triangles is ...

Pabp +Papc = AB +BP +AP + AP +PC +CA

= (AB +BP +PC +CA) +2AP

= Pabc +2AP

Filling in numbers, we have ...

30 +35 = 45 +2AP

20 = 2AP . . . . subtract 45

10 = AP . . . . . . divide by 2

The length of AP is 10 units.