Question

The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden?

Do not include units in your answer.

Answer 1

@AZ

Answer 2

So first the formula
Perimeter of a rectangle = 2 * length * width

Now your question says
length is 4 feet longer than the width

can you write that sentence as an equation?

Answer 3

2 * 4 *192

Answer 4

the perimeter is 192

but first we need to find the length and width
all we know is the relationship between length and width

the length equals to 4 ft more than width

how would we translate this into some math with letter like L and W

Answer 5

is the length 4?

Answer 6

4 * w

Answer 7

Okay I see now

Answer 8

4 feet MORE
NOT 4 times the width

so it's just addition

L = 4 + w

Answer 9

so remember the first formula I mentioned?

Perimeter = 2 * (length + width)

now we have to plug in length = 4 + width

and we'll get

perimeter = 2*(4 + width + width)

and let's just use the variable w for width

perimeter = 2*(4 + w + w)

remember perimeter = 192
so can you solve for w?

Answer 10

192 divided by 2?

Answer 11

so if we do that, we'll get

192/2 = 4 + w + w

what is 192/2 =

Answer 12

96

Answer 13

so we have

96 = 4 + w + w

what is w + w = ?

Answer 14

I don't know what number w is or how to find it

Answer 15

it's just a variable

so if I have one apple + one apple then I have 2 apples

just like that
x + x = 2x

so what is w + w =

Answer 16

2w

Answer 17

exactly! so we have

96 = 4 + 2w

we want to take the 4 to the other side, so what do we do?
Do we have to add 4 on both sides or subtract 4 on both sides?

Answer 18

subtract 4 on both sides

Answer 19

good! so what do we get?

Answer 20

do we subtract 4 from 96 and 2w

Answer 21

we subtract 4 on both sides so like

96 - 4 = 4 + 2w - 4

and so on the right side, the 4 and -4 would cancel out giving us 0 so we're left with

96 - 4 = 2w

does that make sense?

Answer 22

yep

Answer 23

do we keep subtracting

Answer 24

we don't keep subtracting haha

so what is 96 - 4 =

Answer 25

92

Answer 26

good so now we don't have to subtract anymore

92 = 2w

so to find w, divide by 2 on both sides so that we can get w all by itself

Answer 27

46 = 1w

Answer 28

46=w

Answer 29

Good! So now that we know w, we can find the length

remember that sentence we wrote as a math expression/equation
where length was 4 feet more than the width

so
length = 4 + width

what is the length if our width is 46

Answer 30

11.5

Answer 31

mhmmm not sure how you got that

length = 4 + width

width is 46

length = 4 + 46
length = ??

Answer 32

50

Answer 33

yes so now we know

length is 50 feet
width is 46 feet

we want to find the area of the rectangle

area = length * width

can you find the area

Answer 34

2,300

Answer 35

yepp

Answer 36

Yes!