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Points A and B are on side YZ of rectangle WXYZ such that WA and WB trisect ZWX.  If BY = 3 and AZ = 8, then what is the area of rectanlge WXYZ?

 Jul 6, 2022
 #1
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Something like this  :

 

  W                               X

 

 

   Z    8     A          B  3  Y

 

 

If ZWX is trisected, then  angle  AWZ = 30  and  angle  BWZ  = 60

 

So triangle  AZW  is a 30-60-90 right triangle

So WZ = AZ * sqrt 3  =  8sqrt 3 

 

And triangle BZW is a 30 -60-90 right triangle

BZ   =   WZ* sqrt 3  =  8 sqrt 3 * sqrt 3  =  24

 

So   [ WXYZ ]  = [ WZ * ( BZ + BY) ] = [ 8sqrt (3) * ( 24 + 3) ] =   216sqrt (3) units^2

 

cool cool cool

 Jul 6, 2022

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