Question

a. create a design for a garden shaped like a parallelogram. if the area needs to be 150 ft², what dimensions will you choose for the base and height? be sure to include a scale. for example, 1 box = 2 units. b. you want to put a rectangular fence around the entire garden to keep the bunnies out. the fence panels are sold in 1 - foot and 6 - foot panels. how many panels are needed? justify your answer.

Explanation:

Step1: Recall area formula for parallelogram

The area formula for a parallelogram is $A = b\times h$, where $A$ is the area, $b$ is the base and $h$ is the height. Given $A = 150$ square - feet. Let's assume some possible values for $b$ and $h$. If we choose $b = 15$ feet and $h = 10$ feet, $A=15\times10 = 150$ square - feet.

Step2: Consider fence - panel lengths

The fence panels are 1 - foot and 6 - foot panels. For a rectangular (a special case of parallelogram) garden with length $l = 15$ feet and width $w = 10$ feet, the perimeter $P$ of the rectangle is given by $P=2(l + w)$.

Step3: Calculate the perimeter

$P = 2(15+10)=2\times25 = 50$ feet.

Step4: Determine the number of panels

We can use 8 six - foot panels ($8\times6 = 48$ feet) and 2 one - foot panels ($2\times1=2$ feet) to make up the 50 - foot perimeter.

Answer:

A. Dimensions: base = 15 feet, height = 10 feet
B. 8 six - foot panels and 2 one - foot panels. Justification: The perimeter of the rectangular (a type of parallelogram) garden with length 15 feet and width 10 feet is 50 feet. 8 six - foot panels account for 48 feet and 2 one - foot panels account for the remaining 2 feet.