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?
+128460 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
