Question

a gardener has 85 feet of fencing to be used to enclose a rectangular garden that has a border 2 - foot 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 feet. (round to the nearest tenth as needed.) (b) what is the area of the garden? area = (round to the nearest tenth as needed.)

Explanation:

Step1: Let width of garden be $w$.

Length $l = 2w$. The total length of fencing includes the perimeter of the garden and the border. The outer - length $L=2w + 4$ and outer - width $W=w + 4$. The perimeter formula for a rectangle is $P = 2(L + W)$. So $P=2((2w + 4)+(w + 4))=2(3w + 8)=6w+16$. Given $P = 85$ feet.

Step2: Solve for $w$.

Set up the equation $6w+16 = 85$. Subtract 16 from both sides: $6w=85 - 16=69$. Then divide both sides by 6: $w=\frac{69}{6}=11.5$ feet.

Step3: Find the length.

Since $l = 2w$, then $l = 2\times11.5 = 23.0$ feet.

Step4: Calculate the area of the garden.

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

Answer:

(a) Length = 23.0 feet, Width = 11.5 feet
(b) Area = 264.5 square - feet