Question

look at the relationship between the area of the scale drawing and the area of the actual pool. how many square meters are represented by 1 square centimeter? complete the expression to help you solve.

scale	width	length	area
1 cm = 2 m	15 cm	20 cm	300 cm²
1 cm = 10 m	3 cm	4 cm	12 cm²

300·□ = 1,200

Explanation:

Step1: Recall the relationship between scale - length and scale - area

The scale for length is given as \(1\ cm = k\ m\). The scale for area is \((1\ cm)^2=(k\ m)^2\).

Step2: Analyze the second row of the table

The scale is \(1\ cm = 2\ m\). The area of the scale - drawing is \(15\times20 = 300\ cm^2\) and the actual area is \(30\times40=1200\ m^2\).
We know that if \(1\ cm\) represents \(2\ m\), then \(1\ cm^2\) represents \((2\times2)m^2 = 4\ m^2\).
We can also check using the ratio of the actual area to the scale - drawing area. Let \(x\) be the number of square - meters represented by \(1\ cm^2\). We have the proportion \(\frac{1200}{300}=x\).

Step3: Calculate the value

\(\frac{1200}{300}=4\).

Answer:

4