In parallelogram abcd diagonals ac and bd intersect at point e, be = 2x^2 -3x + d = x^2 + 10 what is bd

Answer

Given the statement: In parallelogram ABCD, diagonals AC and BD intersects at point E.

Given that ABCD is a parallelogram.  

As, we know that in a parallelogram diagonals bisect each other.

Since AC and BD intersect at E, and we get E is the mid point of both diagonals AC and BD.

⇒ BE = DE                  .....[1]

Substitute the given values of and in [1] we have;

Subtract on both sides we get;

Simplify:

Subtract 10 on both sides we get;

or

equate these factors equal to zero we get;

(x-5) = 0  and (x+2) = 0

we have;

x = 5 and x = -2

Since, x cannot be negative.

So, x =5

Diagonals BD = BE + DE = 35 + 35 =70 units.

Therefore, the value of BD = 70 units.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet