Question

a gardener has 85 feet of fencing to be used to enclose a rectangular garden that has a border 2 - feet wide surrounding it (see the figure). use this information to answer the following. (a) if the length of the garden is to be twice its width, what will be the dimensions of the garden? the length of the garden is 23.0 feet (round to the nearest tenth as needed.) the width of the garden is 11.5 (round to the nearest tenth as needed.) (b) what is the area of the garden? area = 264.5 square feet (round to the nearest tenth as needed.) (c) if the length and width of the garden is (round to the nearest tenth as needed.)

Explanation:

Step1: Set up perimeter equation for part (a)

Let the width of the garden be $w$ feet. Then the length $l = 2w$ feet. The perimeter of the garden and the border together is considered. The outer - length $L=2w + 4$ and outer - width $W=w + 4$. The perimeter formula is $P = 2(L + W)$. Given $P=85$ feet, so $85=2((2w + 4)+(w + 4))$.

Step2: Simplify the equation

$85=2(2w + 4+w + 4)=2(3w + 8)=6w+16$.

Step3: Solve for $w$

Subtract 16 from both sides: $6w=85 - 16=69$. Then $w=\frac{69}{6}=11.5$ feet. And $l = 2w=23.0$ feet.

Step4: Calculate area for part (b)

The area formula for a rectangle is $A=l\times w$. Substitute $l = 23.0$ feet and $w = 11.5$ feet. So $A=23.0\times11.5 = 264.5$ square feet.

Step5: For part (c)

The dimensions are already found as length $l = 23.0$ feet and width $w = 11.5$ feet.

Answer:

(a) Length: 23.0 feet, Width: 11.5 feet
(b) 264.5 square feet
(c) Length: 23.0 feet, Width: 11.5 feet