In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.
+129852 A little hard to visualize this (I did it with a piece of paper - hope I didn't mess it up !!!)
When we make the fold EF = EA = 9 and EB = 6
And triangle EBF is right so BF = sqrt [ 9^2 - 6^2 ] = sqrt 45 = 3sqrt 5
And FD = BC
And triangle FDC is right with DC = 9 FC = BC - BF = BC - 3sqrt5 = BC - sqrt 45
So
FC = sqrt [ FD^2 - DC^2 ]
(BC - sqrt 45) = sqrt [ BC^2 - 81)
(BC - sqrt 45)^2 = BC^2 - 81
BC^2 - 2*BC*sqrt45 + 45 = BC^2 - 81
-2sqrt (45) BC = -81 - 45
-2 sqrt (45) BC = -126
BC = 126 / ( 2 sqrt 45) = 126 / (2 * 3 * sqrt 5) = 21 / sqrt 5 = (21/5)sqrt 5
