In rectangle ABCD, shown here, CE is perpendicular to BD. If BC = 3 and DC = 8, what is CE?
Using the pythagorean theorem, BD = √73.
DC^2 = DE * DB = DE * √73
64 = DE * √73
BC^2 = BE * DB = BE * √73
9 = BE * √73
9 = (√73 - DE) * √73.
Can you take it from here?
BD = sqrt(BC2 + CD2)
2[BCD] = BC * CD
CE = 2[BCD] / BD
