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

@texaschic101

Answer 2

Well, the sum of 29 and the length of the deck cannot be greater than 134, nor can it be less than that.

Answer 3

So it can be all the numbers between 29 and 134???

Answer 4

@sourwing You're smart...Help me:)

Answer 5

Oh, I'm sorry, let me rephrase that, I did not read it clearly.
Since it cannot be less than 134, we can subtract 29 from 134, giving you 105.
Basically, \[x \ge 105\]
Since the question does not give a maximum, it can be any number of 105 or more.

Answer 6

Hold on, I seemed to have messed up again, one moment.

Answer 7

Alright, so a rectangle has two pairs of opposite congruent sides. Meaning, another side is 29.
\[Perimeter=2l + 2w\]
After solving algebraically, the length must be at least 38 for the perimeter to be at least 134. Therefore, \[Length \ge38\]
Although this seems unrealistic, the possible values are all real numbers 38 or greater.

Answer 8

Alright...a rectangle is a shape with 4 legs....but each opposite leg is equal in length



The perimeter will be the sum of all these legs...

We can say since the Length legs are equal...and the width legs are equal...

Perimeter = 2(Length) + 2(Width)

So this means...if the given width is 29 feet...



This means that ALL we have left...are the LENGTH legs....

So Perimeter = 2(Length) + 2(Width)

We know perimeter = at least 134

and we know Width = 29 so

\[\large 2(Length) + 2(29) \ge 134\]
\[\large 2(Length) + 58 \ge 134\]
\[\large 2(Length) \ge 76\]
\[\large Length \ge 38\]