Question

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 .

What is BD ?

Answer 1

`3x^(2) -x +6`

Explanation:

Given :

BE =
`2x^(2) -x`

DE =
`x^(2) +6`

To Find : Length of BD

Solution :

Refer the attached figure

Since AC and BD intersect at point E

We can see that BD = BE +DE

`BD = 2x^(2) -x +(x^(2) +6)`

`BD = 3x^(2) -x +6`

Thus , Length of BD is
`3x^(2) -x +6`

Answer 2

AC and BC intercept each other at point E. So E is a point on BD.

Then BE + DE = BD. That gives us


`BD = 2x^2-x+x^2+6=3x^2-x+6`

The answer is
`BD=3x^2-x+6`