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Suppose ABCD is an isosceles trapezoid with bases AB and CD and sides AD and BC such that CD > AB. Also suppose that CD = AC and that the altitude of the trapezoid is equal to AB.  Compute AB/CD.

 

 Jan 23, 2021
 #1
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+1

CD^2  =  [ AB + (CD - AB)  / 2 ] ^2  + AB^2

 

CD^2  =   [ AB  + CD ]^2  /  4  + AB^2

 

4CD^2  =  AB^2 + 2AB *CD + CD^2  + 4AB^2

 

3CD^2  = 2AB * CD  + 5AB^2

 

3CD^2   -2AB * CD  -5 AB^2  =   0

 

(3CD  - 5AB)  ( CD + AB)   =   0

 

Either   CD  =  - AB      (reject)    or

 

3CD  - 5AB   = 0

 

3CD   = 5AB

 

AB / CD   =  3 /  5

 

 

cool cool cool

 Jan 24, 2021

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