Question

can someone plz help me out with this algebra question? :D

https://gyazo.com/ab9f947eeb95abf1dd16187af9243426

Answer 1

"The length of a rectangle is 3 times its width"

If W is the width, then what is the length in terms of W?

Answer 2

what??

Answer 3

Let's say the width is 10. If "The length of a rectangle is 3 times its width" then what is the length?

Answer 4

30?

Answer 5

yes you just did

Length = 3*Width

Answer 6

Now we don't know the width. We just call this W

W stands in for any positive real number

Answer 7

make sense?

Answer 8

no :(

Answer 9

If the width is 2, then the length is what?

Answer 10

6

Answer 11

Length = 3*Width
Length = 3*2
Length = 6

Answer 12

yes

Answer 13

How about if the width is 5, what is the length?

Answer 14

5xW
so 5x2
10

Answer 15

times 3 (not times 2)

Answer 16

Length = 3 times Width

Answer 17

oh

Answer 18

The letter W stands in for a number. That's what variables do.

It's similar to what 'x' does

Answer 19

ok

Answer 20

we don't know what number replaces W

Answer 21

so it's just a placeholder for now

Answer 22

Length = 3*Width
L = 3*W

Answer 23

make sense?

Answer 24

yes

Answer 25

Ok we'll now plug that into the perimeter of a rectangle formula
\[\Large P = 2L + 2W\]
\[\Large P = 2(L) + 2W\]
\[\Large P = 2({\color{red}{L}}) + 2W\]
\[\Large P = 2({\color{red}{3W}}) + 2W\]
notice how I replaced the L with 3W. This is valid because L = 3W

Answer 26

ok

Answer 27

We could simplify things out, but there's no need because we're at the answer they want.

Answer 28

thank you

Answer 29

you're welcome