Question

PLEASE HELP!!! The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions? Show your work!

Answer 1

let's call the length of the rectangle L
and let's call the width of the rectangle W

can you write an equation from the first sentence ?
It says "L is 2 cm more than 4 times W "

Answer 2

hmmmmm i think just a second

Answer 3

would it be 4w+2=L

Answer 4

awesome!!!!

Answer 5

ok let's go to the second sentence/question

Answer 6

ok!

Answer 7

the perimeter of the rectangle is 84 cm

Answer 8

The perimeter of a rectangle can be found by adding up all the sides

Answer 9

2 sides will have length L
and
2 sides will have length W

Answer 10

and it will all have to add up to 84 right?

Answer 11

so perimeter of a rectangle can be found by calculating 2L+2W

right so we also have the equation 2L+2W=84

Answer 12

We have a system of equations to solve:

4W+2=L
2L+2W=84


You can do a substitution of the first equation into the second.

Answer 13

you see the first equation is already solved for L
just replace the L in the next equation with what it is equal to

Answer 14

and solve for W first
and we will come back and solve for L

Answer 15

ok so just a minute

Answer 16

k

Answer 17

yeah im not at all sure how to solve for w.....

Answer 18

i thought i did but nope i was really wrong

Answer 19

4W+2=L
2L+2W=84

See that the first equation is L=4W+2
just replace the L in 2L+2W=84 with 4W+2 since you do have L=4W+2


so you have
2(4W+2)+2W=84
this is a linear equation in terms of one variable

Answer 20

First step distribute where you have that 2(4W+2)
distributive law is a(b+c)=a*b+a*c

Answer 21

ok? give me a minute

Answer 22

a(b+c)=a*b+a*c
2(4W+2)=2*4W+2*2=....

Answer 23

ok that makes more sense give me a minute

Answer 24

nope nevermind got something weird idk what i did wrong but i dont think its w = 7

Answer 25

2*4W+2*2=8W+4 did you get this part?

Answer 26

\[2L+2W=84 \text{ where } L=4W+2 \\ 2(4W+2)+2W=84 \\ \\ 8W+4+2W=84 \\ \text{ now combine like terms on the left hand side }\]

Answer 27

uhh yes i did ok um i actually have to go thank you im going to copy this and use it for reference for tonight when i finish this thank you for all your help

Answer 28

Your W was just a little off
I bet you will get it
have a good day

Answer 29

you too!