Question

Chris is building a large deck for the community center. The deck is shaped as a rectangle. The width of the deck is 29 ft. The perimeter of the deck is to be at least 134 ft. (please answer both questions)

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

2) Solve algebraically to find all possible values for the length of the deck.

Answer 1

Question 1)

Width of the deck = W = 29 feet.
Perimeter of the deck = P = At least 134 feet.

We can write the inequality for perimeter as:

$P \geq 134$

Perimeter of rectangle = 2(Length + Width)
Perimeter of given rectangle = 2(Length + 29) = 2(L) + 58

So the inequality that represents all possible values for the length of the deck will be:

$2L+58 \geq 134$

Question 2)

We can solve this inequality to find the range of values for the Length of the deck:

Using the values in inequality we can write: 

$2(L) + 58 \geq 134 \\ \\ 2L \geq 76 \\ \\ L \geq 38$

So this means, for the perimeter to be at least 134 feet the length of the deck must be at least 38 feet.