Answer
See the explanation
Work Step by Step
a.
Design 1-A square means that both the length and the width is equal and the perimeter of a square is 2length plus 2width or equal 4length. Thus, $4l=24ft, l=6$. length$=6$ and the width $=6$.
Area of a square is width times length.
$A_1=6\times6=36ft^2$
Design 2-A circular planter, the circumference of a circle is $C=2\pi r=24ft$ and the area of the circle is $A=\pi r^2$.
Thus, to find the Area from the circumference, we need to find $r$.
$2\pi r=24, r=\frac{12}{\pi}$. Therefore, $A=\pi (\frac{12}{\pi})^2=\pi \frac{144}{\pi ^2}=\frac{144}{\pi}=45.85ft^2$
Therefore, Design 2 will give her larger planting area.
b.
Design 1-the cost of edging material divided by the price of the straight-material a foot is the length of the material bought.
$\frac{120}{3}=40ft$. $4l=40, l=10$
$A_1=10\times10=100ft^2$
Design 2-the cost of edging material divided by the price of the flexible-material a foot is the length of the material bought.
$\frac{120}{4}=30ft$.
$2\pi r=30, r=\frac{15}{\pi}$.
$A_2=\pi \frac{225}{\pi ^2}=\frac{225}{\pi}=71.62ft^2$.
Therefore, Design 1 will give the larger planting area.
