Question

In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, BE=x2−21 , and DE=4x . What is BD ?

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[_] units

Answer 1

it would equal 56

Explanation:

Answer 2

bearing in mind that in a parallelogram, both diagonals bisect each other, namely they cut each other in two equal halves, thus BE = DE. Check the picture below.

we can't use x = -3, because for DE that'd give use a 4(-3) = -12, which doesn't work for a segment with a length greater than 0.

well, since DE = 4(7) = BE, that means BD = DE + BE = 28 + 28 = 56.