# hectictar

+2
30
2
+8956
hectictar  May 29, 2020, 10:02 PM
+2
281
4
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hectictar  Jan 22, 2020
+4
1
1064
3
+8956

hectictar  Sep 9, 2018
+4
1
1066
2
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### Decomposing a Vector

hectictar  Apr 25, 2018
+11
1
1204
4
+8956

### Melody's Birthday!!!

off-topic
hectictar  Apr 15, 2018
+4
1
1064
2
+8956
hectictar  Mar 21, 2018
+7
2909
11
+8956
hectictar  Oct 2, 2017
+2
1
1607
3
+8956
hectictar  Sep 20, 2017
+1
1
1561
2
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hectictar  Apr 25, 2017
+1
1
1559
4
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hectictar  Mar 29, 2017
+2
1
1497
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hectictar  Feb 22, 2017
#2
+8956
+2

We know that

AP / PC  =  1 / 3

We are also given that  AP = 10   so we can substitute  10  in for  AP

10 / PC  =  1 / 3

If it isn't already clear that  PC  must be  30 , we can invert both sides

PC / 10  =  3 / 1

and then multiply both sides of the equation by  10

PC  =  3 / 1 * 10

PC  =  30

And now we can find the length of  AC

AC   =   AP + PC   =   10 + 30   =   40

The diagonals of a square are the same length and bisect each other so...

h   =   AC / 2   =   40 / 2   =   20       where  h  is the height of triangle BPC

Area of triangle BPC   =   ( 1/2 )( PC )( h )   =   ( 1/2 )( 30 )( 20 )   sq units   =   300   sq units

Oct 5, 2019