Question #8f558

1 Answer
Axelalexbros
Nov 30, 2017

I will assume that 2x2 is #2x^2#, BD = 13.11737692 or 35.24695076

Explanation:

One of the properties of a parallelogram is that the diagonals of this polygon bisect each other. Diagonal BD is bisected into BE and DE.
BE and DE must be equal because they are segments form bisection.

BE = DE or #2x^2-3x=2x+10#

This is a quadratic, so lets put this into a more friendly form

#2x^2-5x-10=0#
We will plug this into the quadratic formula
#(-b+-sqrt(b^2-4ac))/(2a)#
#(-(-5)+-sqrt((-5)^2-4(2)(-10)))/(2*(2))#
#(5+-sqrt(25+80))/(4)#
#(5+-sqrt(105))/4#
#x=3.811737691# or #-1.311737691#
plug -5.24... into both and you get a positive number, so both solutions are correct.

Plug into formula for BD, or BE+DE

Also BE=DE
So BE+BE=BD
2DE=BD
#2(2x+10)=BD#
#4x+20=BD#

BD = 14.75304924 or 35.24695076

Hope this helps.

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