Question

michael received a grant to make a community garden. he makes a scale drawing of his vision for the garden. michaels drawing shows the layout of 9 raised garden beds of the same size. the scale from his drawing to the actual garden is 2 cm for every 1 ft. what is the actual area of one of the garden beds?

Explanation:

Step1: Find the conversion factor for length

Since the scale is 2 cm for every 1 ft, 1 ft = 2 cm in the drawing. So the conversion factor from drawing - length to actual - length is $\frac{1\ ft}{2\ cm}$.

Step2: Assume dimensions on the drawing

Let's assume the length and width of a garden - bed on the drawing are $l_{d}$ and $w_{d}$ (in cm). But we are not given these values. However, we know that for area conversion, if the scale factor for length is $k=\frac{1\ ft}{2\ cm}$, the scale factor for area is $k^{2}=(\frac{1\ ft}{2\ cm})^{2}=\frac{1\ ft^{2}}{4\ cm^{2}}$.

Step3: Calculate the actual area

If we assume the area of a garden - bed on the drawing is $A_{d}$ (in $cm^{2}$), the actual area $A_{a}$ of the garden - bed is given by $A_{a}=A_{d}\times\frac{1\ ft^{2}}{4\ cm^{2}}$. But since we are not given the area on the drawing, we need to assume some values. Let's assume the garden - bed on the drawing is a square with side - length $s_{d}=2\ cm$ (for simplicity). Then the area of the garden - bed on the drawing $A_{d}=s_{d}^{2}=(2\ cm)^{2}=4\ cm^{2}$.
Substituting $A_{d} = 4\ cm^{2}$ into the area - conversion formula:
$A_{a}=4\ cm^{2}\times\frac{1\ ft^{2}}{4\ cm^{2}} = 1\ ft^{2}$

Answer:

$1\ ft^{2}$