Jeremy is building a deck for the community center. The deck is shaped as rectangle. The width of the deck is 29ft. The perimeter of the deck is to be at least 134ft. Write an inequality that represents all possible values of the length of the deck. Find all possible values for the length of the deck.
One correction in second line .
P > 134 ft
120
To find the inequality that represents all possible values of the length of the deck, we can use the formula for the perimeter of a rectangle, which is given by P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, we know that the width of the deck is 29ft, so we can substitute W = 29 into the formula: P = 2L + 2(29).
The problem states that the perimeter of the deck is to be at least 134ft. So we can write the inequality as follows:
2L + 2(29) ≥ 134
To find all possible values for the length of the deck, we can solve this inequality for L.
First, distribute the 2: 2L + 58 ≥ 134.
Next, subtract 58 from both sides of the inequality: 2L ≥ 76.
Finally, divide both sides of the inequality by 2: L ≥ 38.
Therefore, the inequality that represents all possible values of the length of the deck is L ≥ 38.
In other words, the length of the deck must be greater than or equal to 38 feet.
W = 29 ft
P = 134 ft
P = 2 L + 2 W = 2 ( L + W )
P > 134 ft
2 ( L + 29 ) > 134
2 L + 58 > 134 Substract 58 to both sides
2 L + 58 - 58 > 134 - 58
2 L > 76 Divide both sides by 2
L > 38 ft