Question

6 michael received a grant to make a community garden. he makes a scale drawing of his vision for the garden. michael’s drawing shows the layout of 9 raised garden b 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 o of the garden beds?

Explanation:

Step1: Find the conversion factor for length

The scale is 2 cm for every 1 ft. So, 1 ft = 2 cm.

Step2: Assume dimensions of garden - bed on drawing

Let's assume the length and width of a garden - bed on the drawing are \(l_{d}\) and \(w_{d}\) (in cm). Since no dimensions of the garden - bed on the drawing are given, we'll work with the general conversion. If we assume the length of a garden - bed on the drawing is \(l_{d}\) cm and width is \(w_{d}\) cm.
The actual length \(l_{a}\) (in ft) and width \(w_{a}\) (in ft) of the garden - bed can be found using the scale. We know that if \(l_{d}\) is the length on the drawing, then \(l_{a}=\frac{l_{d}}{2}\) ft and \(w_{a}=\frac{w_{d}}{2}\) ft.
The area of a rectangle \(A = l\times w\). The actual area \(A_{a}\) of the garden - bed (in square feet) is \(A_{a}=l_{a}\times w_{a}=\frac{l_{d}}{2}\times\frac{w_{d}}{2}=\frac{l_{d}w_{d}}{4}\) square feet.
Since no dimensions of the garden - bed on the drawing are provided in the problem, we can't give a numerical answer. But if we assume the length and width of a garden - bed on the drawing are \(l_{d}\) and \(w_{d}\) (in cm), the formula for the actual area of one garden - bed in square feet is \(\frac{l_{d}w_{d}}{4}\) square feet.

If we assume some values for \(l_{d}\) and \(w_{d}\), for example, if \(l_{d} = 10\) cm and \(w_{d}=8\) cm:

Step3: Calculate actual length and width

The actual length \(l_{a}=\frac{10}{2}=5\) ft and the actual width \(w_{a}=\frac{8}{2} = 4\) ft.

Step4: Calculate actual area

The actual area \(A_{a}=l_{a}\times w_{a}=5\times4 = 20\) square feet.

Answer:

If the length and width of a garden - bed on the drawing are \(l_{d}\) cm and \(w_{d}\) cm respectively, the actual area of one garden - bed is \(\frac{l_{d}w_{d}}{4}\) square feet. If \(l_{d} = 10\) cm and \(w_{d}=8\) cm, the actual area is 20 square feet.