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Triangle \( ABC\) has coodinates \(A= (-4, 0)\), \(B= (4 , 0)\), and \(C= (0 , 3)\).

Let \(P\) be the point in the first quadrant such that \(\triangle ABP\) has half the area of \(\triangle ABC\) but both triangles have the same perimeter.

What is the length of \(CP?\)

 

 Dec 27, 2020
 #1
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 Dec 27, 2020
edited by CPhill  Dec 27, 2020
 #2
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Perimeter of ΔABC = 18 units and the area = 12 square units.

 

AB = 8

 

AP = 8.4641

                            

BP = 1.5359

 

AB + AP + BP = 8 + 8.4641 + 1.5359 = 18

 

Area of ΔABP = 6 u2

 

CP ≈ 4.582456 units

 Dec 27, 2020

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