Question

The kid's garden in my yard has a length that is two feet longer than its width and is surrounded by a uniform stone border that is 1 foot wide. This summer I plan on enclosing the entire piece of land (garden and stone) with a fence. Find the dimensions of the enclosed piece of land if its area is 65 square feet. If fencing costs $12.25 per foot, how much will it cost me to put fencing around the entire enclosed piece of land?

A. Width: 6 feet, Length: 8 feet, Cost: $570.25
B. Width: 5 feet, Length: 7 feet, Cost: $483.75
C. Width: 7 feet, Length: 9 feet, Cost: $665.75
D. Width: 4 feet, Length: 6 feet, Cost: $398.25

Answer 1

The garden's width is 5 feet, and the length is 7 feet after accounting for the stone border. However, the total cost of the fencing, based upon the fencing price of $12.25 per foot, is calculated to be $294.00, not the $483.75 listed in option B.

Step-by-step explanation:

Let's denote the width of the garden by w feet. Then the length would be w + 2 feet. The stone border adds 1 foot to each side of the width and the length, resulting in a total width of (w + 2) feet and a total length of (w + 4) feet for the enclosed land. The area of the enclosed piece of land is therefore (w + 2)(w + 4) square feet.

To find the dimensions that give an area of 65 square feet, we set up the equation and solve for w:
(w + 2)(w + 4) = 65.

This simplifies to w^2 + 6w + 8 = 65, w^2 + 6w - 57 = 0. Factoring, we find (w - 5)(w + 11) = 0, which provides the possible widths of 5 feet (since width can't be negative). Hence, the length is 5 + 2 = 7 feet.

The perimeter of the enclosed land is twice the sum of the width and length, 2(w + 2 + w + 4), which equals 2(5 + 7) or 24 feet. Multiplying this by the cost of fencing, which is $12.25 per foot, gives us the total cost: 24 feet × $12.25/foot = $294.00.

The correct answer is B. Width: 5 feet, Length: 7 feet, Cost: $483.75. However, based on our calculation, the cost seems incorrect, which is $294.00 based on the given fencing price. The student should recheck the calculations or the cost per foot of the fence.