Question

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

What is BD ?

Answer 1

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 $BD=3x^2-x+6$

Answer 2

Answer:

$3x^{2} -x +6$

Step-by-step 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 $3x^{2} -x +6$