Question

Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. She knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. Which equations represent this relationship? Check all that apply.
x + one-half x = 18
2 x + x = 18
2 (x) + 2 (2 x) = 18
x + one-half x + x + one-half x = 18
2 (x + one-half x) = 18
2 x + one-half x = 18

Answer 1

Which one do you think it is?

Answer 2

Well, from what we know, the perimeter is 18

Answer 3

I think its is the 2,3

Answer 4

and the width is 1/2(length)

Answer 5

perimeter = 2width + 2length

Answer 6

So try setting it up like this:
2(width)+2(length) = 18
2(1/2 length)+ 2(length)

Answer 7

Do you see where this comes from?

Answer 8

We can write the question is terms of width AND length. Rn we are doing in terms of length

Answer 9

yes

Answer 10

Okay, so we have 2(1/2 length)+ 2(length) = 18
One variable, so we can solve for that
2(1/2) = 1
so length + 2 length = 3 length
length + 2 length = 18

Answer 11

You can replace length for x, does this match any of your answer choices?

Answer 12

one of them

Answer 13

Yes the 2nd one

Answer 14

Now we can eliminate some answer choices that aren't possible

Answer 15

we have stated that the length is x, and that is the only variable. So we know
2 x + x = 18 is true.
So can this be true then?
x + one-half x = 18 ???

Answer 16

@lizzie777
What I am asking is that knowing that the second answer choice is right. Can the first also be right?

Answer 17

I could be

Answer 18

x + one-half x = 18
2 x + x = 18

Well since both of the above equations are equal to 18, you can set them equal to each other.
x+ 1/2x = 2x+x
add like terms
3x = 3/2x

Answer 19

3x = 3/2 x only when x is zero, right?
but the perimeter is 18 so answer 1 is incorrect

Answer 20

Lets make it quicker. You want equations that are similar to
2 x + x = 18, can you spot any off the bat?

Answer 21

its the second one

Answer 22

there can be more answer choices than the second one

Answer 23

the 4 one?

Answer 24

I am asking if any of the other answer choices are like the second one
that is, rewritting 2 x + x = 18

Answer 25

Yes the fourth one is also correct

Answer 26

Can you spot anymore?

hint: try looking at the 5th one

Answer 27

I know its not the first one

Answer 28

the 5 one look like it could be

Answer 29

try rewritting the 5th one. It is also equal to 18.
So set the 5th one equal to the 2nd one and see if you can get something like 1 =1

Answer 30

I have to go I''ll be right back

Answer 31

here, Ill help you.

2 (x + one-half x) = 18
2x+x=18
2(x+1/2x) = 2x+x
2x+x = 2x+x
0 = 0

Answer 32

So that means that the 5th one is also correct

Answer 33

You are done! Good job persisting.
correct answers: 2, 4,5

Answer 34

thank you so much

Answer 35

do you want to be friends

Answer 36

No problem

Answer 37

Ya got any other questions?

Answer 38

I''l let you know when I get back