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In rectangle ABCD, shown here, CE is perpendicular to BD. If BC = 3 and DC = 8, what is CE?

 

 Aug 2, 2021
 #1
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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?

 Aug 2, 2021
 #2
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BD = sqrt(BC2 + CD2)

 

2[BCD] = BC * CD

 

CE = 2[BCD] / BD

 Aug 2, 2021

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