Question

. Jeremy is building a large deck for a community center. The deck is shaped as a rectangle. The width of the deck is 29 feet. The perimeter of the deck is to be at least 134 feet.

a. Write an inequality that represents all possible values for the length of the deck.






b. Find all possible values for the length of the deck.

Answer 1

I just need help solving it, I don't want the answer just need help :P

Answer 2

let L represent length and W represent width
perimeter = L +W +L +W = 2L + 2W

the deck is to be at least 134 feet, thus perimeter is greater or equal 134

Answer 3

can you solve it now ?

Answer 4

im trying one sec.

Answer 5

ok, tell me what you get to check it for you

Answer 6

so 58W*X2?

Answer 7

what's X ?

Answer 8

"let L represent length and W represent width
perimeter = L +W +L +W = 2L + 2W" Very nice.

Note that the width of the deck is a fixed 29 feet. Substitute 29 ft. for W.

@hoblos: "the deck is to be at least 134 feet, thus perimeter is greater or equal 134" doesn't make sense. Please reread the original question and fix this.

@letsparty: Where did "so 58W*X2?" come from? Please explain your reasoning. Why not use W and L as your variables?

Answer 9

I did 29+29 to get my width

Answer 10

sorry 58W*L2

Answer 11

ohh you're right @mathmale my bad i forgot 2 words !
so it is
"the perimeter of the deck is to be at least 134 feet, thus perimeter is greater or equal 134"

Answer 12

@letsparty: The width (W) of the deck is 29.
Thus, the perimeter will be twice that, plus twice the length.

Write that out in symbols, please.

Answer 13

it is
2L + 2W @letsparty

now replace W by 29
what do you get ?

Answer 14

29+29+L+L=58*L*L

Answer 15

Right start. But where does this multiplication ( * ) come from?

Answer 16

so just 58+L+L

Answer 17

yeah now it's correct

Answer 18

Yes, or 58+2L. Please label this expression. What's it for?

Answer 19

to find the perimeter of the deck

Answer 20

Right. @hoblos, what next?

Answer 21

so we find the expression of the perimeter, and we already figured out that it has to be greater or equal to 134

so what is the inequality that we get ?

Answer 22

so can I do 134/2? to find L?

Answer 23

before that, we must write the inequality

Answer 24

What does "greater than or equal to 134" mean? Explain.

Answer 25

it has to be atlease 134 or 135+

Answer 26

It has to be at least 134.
What has to be at least 134?

Answer 27

the Total Deck

Answer 28

What is the symbolic way of writing "at least 134"?

Answer 29

We're discussing the dimensions of the deck, remember? Not "the total deck."

Answer 30

</=

Answer 31

From earlier: 58+2L represents the PERIMETER of the deck.
The perimeter must be at least 134.

Write the appropriate inequality.

Answer 32

"<" is LESS than
">" is GREATER than

Answer 33

hmm....so 58+76?

Answer 34

we are trying to find an inequality

we find that P = 58 + 2L
and we know that P >= 134

if we replace P by 58 + 2L in the inequality, what do we get ?

Answer 35

so 134>=58+2L?

Answer 36

what you wrote means: "134 is greater or equal to the perimeter"

we actually need the opposite
58+2L mus be greater than or equal 134

Answer 37

im confused..

Answer 38

lets try again

P = 58 + 2L
do you understand how we got this ?

Answer 39

yes

Answer 40

good,
the question is saying "The perimeter of the deck is to be at least 134 feet"

this means P >= 134

you understand this one ?

Answer 41

yes P is at lease 134 and greater then 134 correct?

Answer 42

yeah, "at least 134" means "greater than or equal 134"

Answer 43

ok I get it

Answer 44

great
so if we replace P by "58 + 2L" what will we get ?

Answer 45

78

Answer 46

keep it as inequality don't solve it

Answer 47

58+2L>=134

Answer 48

Greatt! that's the inequality that we need

now if we subtract 58 from both sides, what do we get?

Answer 49

2L=78

Answer 50

recalculate 134-58= ?

Answer 51

2L=76

Answer 52

where is the ">" sign ?

Answer 53

2L>=76

Answer 54

Great

now divide both sides by 2

Answer 55

L=38

Answer 56

because we're looking for an inequality in L (not an equation)

Answer 57

you missed the ">" again

Answer 58

gahh L>=38

Answer 59

Great job!

Answer 60

sweet!! thanks Hoblos! and Thanks mathmale!!

Answer 61

glad to help! :)