Solve the problem.
-A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 276 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
A) 9,522 ft2
B) 19,044 ft2
C) 14,283 ft2
D) 4,761 ft2

Question

Quizplus · Accepted Answer

The largest area that can be enclosed by a given perimeter is a square. However, since one side is not fenced, the optimal shape becomes a rectangle where the length is twice the width. The total fencing available is 276 feet, which will be used for two widths and one length. Let the width be $w$ and the length be $2w$. The perimeter equation is $2w + 2w = 276$, simplifying to $4w = 276$, so $w = 69$ feet. The length is $2w = 138$ feet. The area is $w \times 2w = 69 \times 138 = 9,522$ square feet.

Solve the Problem. -A Developer Wants to Enclose a Rectangular Grassy Lot That