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ABCD is a trapezoid. E is the midpoint of CD and F is the midpoint of AB. Find the length of BC and show your work. If CD is 24, what is the length of CE. Explain how you calculate your answer.

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Respuesta :

Let 

AB = 2x 

CD = 2y 

BC = h 

Then for AFED 

y^2 = x^2 + (16 - 12)^2 

y^2 = x^2 + 16 ...........(1) 

For BCEF 

y^2 = x^2 + (12 - h)^2 ........(2) 

Equating equations (1) and (2) 

x^2 + (12 - h)^2 = x^2 + 16 

(12 - h)^2 = 16 

h^2 - 24h + 144 = 16 

h^2 - 24 + 128 = 0 

(h - 16)(h - 8) = 0 

h = 16 , 8 

h = 16 is obviously not a solution 

Hence BC = 8 


CD = 2CE 

24 = 2CE 

CE = 12

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