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. Solve algebraically to find all possible values for the length of the deck. SHOW ALL WORK

Answer 1

By definition, the perimeter of a rectangle is given by:

$P = 2w + 2l$

Where,

w: width of the rectangle

l: length of the rectangle

We write then the inequality that represents the problem:

$2l + 2 (29)\geq 134$

Rewriting we have:

$l + 29\geq 67$

Then, solving the inequality for "l" we have:

$l\geq 67 - 29$

$l> = 38$

Therefore, the length must be at least 38 feet.

Answer:

An inequality that represents all possible values for the length of the deck is:

$l + 29\geq 67$

The possible values for the length of the deck is:

[38, inf)