In parallelogram abcd , be=7x−2 and de=x^2−10.segment ac intersects segment bd at point e. what is bd ? enter your answer in the box.

Length of BD = 108 units

Step-by-step explanation:

Given: In parallelogram ABCD , BE = 7x-2 and DE = .

Segment AC intersects segment BD at point E.

Properties of parallelograms:-

The diagonal BD;

BD = BE + ED

since, by properties of parallelogram;

BE = ED                     ......[1]

Substitute the given values of BE and DE in [1] to solve for x;

or

(x-8)(x+1) = 0

equate each factor equals to 0 we get;

x = 8 and x = -1

Since sides are always in positive,

⇒x =8

Then;

BE = 7x -2 = 7(8) -2 = 56-2 = 54 units.

To find the Length of BD:

As we know;

BD = BE + ED = BE + BE = 2BE              [Since, BE = ED]

BD = units

Therefore, the length of BD is 108 units.