Question

the perimeter of a rectangle is 26ft. the length is 9 ft longer than the width. find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width.
write the first equation.
2x+2y=
write the second equation
x=y +_____.
what is the length? ___ ft
what is the width? ____ft

Answer 1

Let's let P rep. the perimeter, l rep. the length, and w rep. the width.

We know from the question that P = 26

We also know that because it is a rectangle: P = 2*l + 2*w

Therefore 26 = 2*l + 2*w

The second equation tells us that the length is 9ft longer than the width:

Therefore l = w + 9

Does that help?

Answer 2

I didn't read the question:

replace x with l and y with w

Answer 3

do you know what 2x+2y= and x=y+____, what is the length? ___ft
what is the width? ___ft

Answer 4

I was hoping you could tell me.

Since you have two equations and two "unknowns" you can solve for them.

Try isolating for w or l and substituting that into the other equation.

Answer 5

i'm lost on this question

Answer 6

did you understand my first hints?

"Let's let P rep. the perimeter, l rep. the length, and w rep. the width.

We know from the question that P = 26

We also know that because it is a rectangle: P = 2*l + 2*w

Therefore 26 = 2*l + 2*w

The second equation tells us that the length is 9ft longer than the width:

Therefore l = w + 9"

???

Answer 7

no, I am horrible at math

Answer 8

Ok, do you understand what it means to let a variable represent a number. In this case a measurement in feet ?

Answer 9

no

Answer 10

a variable is just a letter we use in math to represent a number that we don't necessarily know

Answer 11

ok

Answer 12

so we are trying to find a length and a width so I'll call them L and W

Answer 13

ok

Answer 14

(and P will represent the perimeter)

Answer 15

Perimeter is the total distance around something

Answer 16

ok

Answer 17

Rectangles have two longer sides(lengths) and two shorter sides(widths) right?

Answer 18

yes

Answer 19

So
P = L + L + W + W
right?

Answer 20

ok

Answer 21

this is the same as saying:
P = 2L + 2W
right?

Answer 22

yes

Answer 23

cool

Answer 24

so because the perimeter is given in the equation we can change this from:
P = 2L + 2W
to:
26 = 2L + 2W

Answer 25

ok

Answer 26

excellent. that is 1 of the 2 equations.

Now the next one:

since the length(L) is 9 feet longer than the width(W) we know that the width + 9 feet is the length

do you follow?

Answer 27

but how do we get to the answer 2x+2y=___?

Answer 28

that we got from the first equation.

Since x and y and length and width:

26 = 2L + 2W is the same as 2L + 2W = 26 or 2X + 2Y = 26

Answer 29

oh ok

Answer 30

are we working on how to get x=y +___?

Answer 31

yes

Answer 32

ok

Answer 33

if the length and width were the same then this would be true right?
L = W

Answer 34

yes

Answer 35

you still there?

Answer 36

yes, sorry.

now since the length is 9 feet longer than the width we can say that the width plus 9 is the length. right?

Answer 37

yes

Answer 38

great, this statement:
"the width plus 9 is the length"

is the same as the equation:
L = W + 9

Answer 39

ok

Answer 40

now you have both equations:
26 = 2W + 2L
and L = W + 9

Answer 41

so is it x=y+9?

Answer 42

yes!

Answer 43

ok

Answer 44

so how do we now get the length and width?

Answer 45

you still there?

Answer 46

yes, sorry answering two questions at once.

Now,

isolate for one of the variables in one of the equations:

L = W + 9
(this is already isolated for L, yey!, don't have to do anything)

let's put this into the other equation:

everywhere I see L I'll replace it with W + 9

Answer 47

ok

Answer 48

so doing that:

2W + 2L = 26
2W + 2(W + 9) = 26

Answer 49

so the width = 26?

Answer 50

or 35?

Answer 51

2W + 2(W + 9) = 26

distribute:
2W + 2W + 18 = 26

subtract 18 from both sides:
2W + 2W + 18 -18 = 26 - 18

on the left side the 18s cancel:
2W + 2W = 26 - 18

on the right side we subtract:
2W + 2W = 8

collect the w's:
4W = 8

divide both sides by 4:
(4/4)W = 8/4

simplify:
W = 2

Answer 52

so width = 2 ft?

Answer 53

sttill there, I only have 5 more minutes on the computer to finish this question?

Answer 54

yes 2ft.

now solve for L:
26 = 2L + 2W
26 = 2L + 2(2)
26 = 2L + 4
26 -4 = 2L
22 = 2L
L = 11

Answer 55

so length is 11 ft?

Answer 56

yes

Answer 57

okay, i really appreciate your help. thank you very much

Answer 58

no problem. you'll get the hang of it