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ABCD is a square with AC = 49.5 cm. P is a point inside ABCD such that PB = PC, and the area of triangle PCB is one third of the area of ABCD. What is the length, in cm., of PA? Round your answer off to the nearest integer.

 Apr 9, 2021
 #1
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PA = 21.03345549

or

PA ≈ 21 cm

smiley

 Apr 10, 2021
 #2
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If AC    = 49.5 cm......the  the  side of the square  is   49.5 / sqrt 2 cm  ≈  35 cm

 

And  the area  of the  square =  35^2  ≈  1225  cm^2

 

1/3  of  this is ≈  408.33  cm^2

 

Since PB  = PC......then triangle PBC is isoceles  and its height  can  be  found  as

 

408.33 =  (1/2) BC  * height

 

816.66  =  35  * height

 

816.66 / 35  =  height ≈   23.33 cm

 

Call the  point  P ,  ( 35 - 23.33 , 17.5)   =  ( 11.67, 17.5)

 

Let  A  =   (0, 35)

 

So  PA =    sqrt    [ ( 11.67 - 0 )^2  +  ( 35  -17.5)^2   ]   ≈   21 cm

 

 

cool cool cool

 Apr 10, 2021

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