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mrs_skeptik [129]
2 years ago
7

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

Mathematics
1 answer:
Mazyrski [523]2 years ago
8 0

Answer:

  10

Step-by-step 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.

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