Question

7. 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

The perimeter of a rectangle is 2 times its width plus 2 times its length
\[\large P = 2w+2l \]

So if the perimeter has to be 'at least' 134 feet what do you think the inequality will look like?

Answer 2

If the perimeter were going to be equal to 134 what would the equation be?

Answer 3

so... 134 = 2 x 33.5 + 2 x 33.5

Answer 4

We know the width is 29 feet

Answer 5

134 = 2x29 + 2 x 37.5?

Answer 6

Let's just leave it as
\[134 = 58 + 2l\]
Now that equal sign should be <, <=, >,= or >=

The perimeter should be at least 134 so which should it be?

Answer 7

> the perimeter would be dubble l+W

Answer 8

Here, 58 + 2L represents the actual perimeter of the fence and 134 represents what the perimeter should be at the least

Answer 9

So the options would be

58 + 2L > 134
58 + 2L >or= 134
58 + 2L < 134
58 + 2L <or= 134
58 + 2L = 134

Based off of them saying that it should at the least be 134 which inequality do you think it is?

Answer 10

Can the perimeter of the fence be less than 134?

Answer 11

58 + 2L >or= 134

Answer 12

Yep :D

Answer 13

sorry son was srying

Answer 14

That's fine

Answer 15

Now isolate the L in 58 + 2L >or= 134

Answer 16

134-58 = 76
2l<76
l<76/2
l<38

Answer 17

not sure what it means by finding all possible values.

Answer 18

All possible values for l with the W of 29 are all the values that are greater than 38.

Answer 19

figured it out thanks hunus

Answer 20

Yup :)