Question

The following table shows the length and width of two rectangles:


Length Width
Rectangle A x + 8 x − 1
Rectangle B 4x + 5 3x − 2


Which expression is the result of the perimeter of rectangle B minus the perimeter of rectangle A?
10x − 12
18x + 32
10x − 8
18x + 6

Answer 1

can someone help me on this?? i dont understand it

Answer 2

Yikes! A little scary, huh? Not to worry though, it's actually pretty easy. Let's take it one step at a time.

Answer 3

ok great

Answer 4

The question sounds very confusing, "the perimeter of rectangle B minus the perimeter of rectangle A"... uh.. yeah. Let's just ignore that for now and think about the perimeters separately:

Perimeter of rectangle A is (we will find out)

and

Perimeter of rectangle B is (again, we will find that out).

Answer 5

okay

Answer 6

So, what do we know about rectangle A? The table says that
A's length is x + 8 (some number) and the width is x - 1 (some other number).

Let's draw a picture so we can see what this even means.

Answer 7

Alright, does that picture make sense so far?

Answer 8

yes, it does

Answer 9

OK, perfect! We are almost done with the hardest part. Do you remember how to find the perimeter?

Answer 10

you time it by each side ??

Answer 11

times*

Answer 12

Close, that's the area (they often get confused). :)

Answer 13

It's actually easier... we just add all four sides together and measure the outside of the rectangle.

Answer 14

ooh okay

Answer 15

(x+8) + (x-1) + (x+8) + (x-1) = 4x + 16 - 2 = 4x + 14. There that's better.

Answer 16

So that is the perimeter of A. Any questions on how we did that part?

Answer 17

nope

Answer 18

OK. Now, we just do exactly the same thing for rectangle B.

Answer 19

We have different numbers:
B width = 3x - 2
B length = 4x + 5

Answer 20

awesome

Answer 21

And, then we just add all four sides... it's a little messy, but try it and see what you get. I'll check your answer. :)

Answer 22

ok give me a second

Answer 23

sure thing. take your time. :)

Answer 24

4x+5+3x-2+4x+5+3x-2= 14x+6

Answer 25

Excellent! Good job!

Answer 26

Alright, so now we know that:
Perimeter of A = 4x + 14
Perimeter of B = 14x + 6.

Answer 27

so subtract 14x+6- 4x+14

Answer 28

?

Answer 29

Good, but be careful with your parentheses. We want the whole perimeter of A to be subtracted so we need
(14x + 6) - (4x + 14) in order to get the right answer.

Answer 30

so its 10x-8 ??

Answer 31

Exactly!

Answer 32

YAYYY THANKYOU SO MUCH :))

Answer 33

You're welcome! Good job!

Answer 34

:)