Answer:
Part 1) [tex]x=6[/tex]
Part 2) [tex]x=5,75[/tex]
Part 3) [tex]NO=80\ units[/tex]
Part 4) [tex]x=3,5[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
GH=FE
substitute the given values
[tex]2x+10=22[/tex]
solve for x
subtract 10 both sides
[tex]2x=22-10[/tex]
[tex]2x=12[/tex]
Divide by 2 both sides
[tex]x=6[/tex]
Part 2) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
FG=EH
substitute the given values
[tex]4x+5=28[/tex]
solve for x
subtract 5 both sides
[tex]4x=28-5[/tex]
[tex]4x=23[/tex]
divide by 4 both sides
[tex]x=5,75[/tex]
Part 3) What is the length of NO?
step 1
Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
NO=ML
substitute the given values
[tex]4x+20=2x+50[/tex]
solve for x
Group terms
[tex]4x-2x=50-20[/tex]
[tex]2x=30[/tex]
Divide by 2 both sides
[tex]x=15[/tex]
step 2
Find the value of NO
we have that
[tex]NO=4x+20[/tex]
substitute the value of x
[tex]NO=4(15)+20=80\ units[/tex]
Part 4) we know that
The diagonals in a parallelogram bisect each other
so
LB=BN
LN=LB+BN ----> by addition length postulate
LN=2LB
substitute the given values
[tex]2x+5=2(6)[/tex]
solve for x
[tex]2x+5=12[/tex]
subtract 5 both sides
[tex]2x=12-5[/tex]
[tex]2x=7[/tex]
Divide by 2 both sides
[tex]x=3,5[/tex]
