Question

the scale is 1 cm = 5 m. both the length and width are multiplied by 5 to find the length and width of the actual pool. if we multiply the dimensions by 5, that means that the area of the scale drawing will be multiplied by 5² to find the area of the actual pool.
scale width length area
1 m = 1m 30 m 40 m 1,200 m²
1 cm = 5 m 6 cm 8 cm 48 cm² 1 cm² =?m²
48·□=1,200
10 5² 10²

Explanation:

Step1: Recall area - scale relationship

When the linear - scale factor is $k$, the area - scale factor is $k^{2}$. Here, the linear - scale factor from the scale drawing to the actual is $k = 5$ (since $1\ cm$ on the scale drawing represents $5\ m$ in real - life), so the area - scale factor is $k^{2}=5^{2}$.

Step2: Check the relationship between scale - drawing area and actual area

Let the area of the scale drawing be $A_{s}=48\ cm^{2}$ and the area of the actual pool be $A_{a}=1200\ m^{2}$. We know that $A_{a}=A_{s}\times k^{2}$. Substituting the values, we have $1200 = 48\times k^{2}$. Solving for $k^{2}$, we get $k^{2}=\frac{1200}{48}=25 = 5^{2}$.

Answer:

$5^{2}$