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In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, BE=2x2−3x , and DE=x2+10 .

What is BD ?

 

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 units

Guest Dec 13, 2017
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The diagonals of a parallelogram bisect each other....therefore

 

2x^2 -3x  = x^2 + 10    simplify

 

x^2 - 3x - 10  = 0    factor

 

(x -5)(x + 2)   = 0

 

Setting each linear factor to 0 and solving for x....we have two possibilities, x  = 5  or x  = - 2

 

If  x  = 5,  BD  =  2 [ (5)^2 + 10 ]  =  70

 

If x  = -2, BD  = 2 [ (-2)^2 + 10 ] =  28

 

 

cool cool cool

CPhill  Dec 13, 2017

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