Question

1. what is x? (picture 1 and 2)

2. What is the length of NO? (3rd picture)
3. If LB = 6 and LN = 2x+5, what is x? (fourth picture)

Answer 1

Part 1)
`x=6`

Part 2)
`x=5,75`

Part 3)
`NO=80\ units`

Part 4)
`x=3,5`

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

`2x+10=22`

solve for x

subtract 10 both sides

`2x=22-10`

`2x=12`

Divide by 2 both sides

`x=6`

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

`4x+5=28`

solve for x

subtract 5 both sides

`4x=28-5`

`4x=23`

divide by 4 both sides

`x=5,75`

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

`4x+20=2x+50`

solve for x

Group terms

`4x-2x=50-20`

`2x=30`

Divide by 2 both sides

`x=15`

step 2

Find the value of NO

we have that

`NO=4x+20`

substitute the value of x

`NO=4(15)+20=80\ units`

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

`2x+5=2(6)`

solve for x

`2x+5=12`

subtract 5 both sides

`2x=12-5`

`2x=7`

Divide by 2 both sides

`x=3,5`