Question

Match the scale drawing and the actual area to the correct scale.

Column 1	Column 2
scale drawing area: $13$ square inches actual area: $117$ square feet	$1$ inch to $4$ feet
scale drawing area: $5$ square inches actual area: $125$ square feet	$1$ inch to $3$ feet
scale drawing area: $8$ square inches actual area: $128$ square feet	$1$ inch to $5$ feet
scale drawing area: $12$ square inches actual area: $48$ square feet	$1$ inch to $2$ feet

Answer 1

Step-1: Find the ratio of scale drawing area to actual area in each case:

$\left(\mathrm{A}\right)$ $\frac{13}{117}=\frac{1}{9}$ (reduce to simplest form)

$\left(\mathrm{B}\right)$$\frac{5}{125}=\frac{1}{25}$ (reduce to simplest form)

$\left(\mathrm{C}\right)$$\frac{8}{128}=\frac{1}{16}$ (reduce to simplest form)

$\left(\mathrm{D}\right)$$\frac{12}{48}=\frac{1}{4}$ (reduce to simplest form)

Step-2: Find the square of the scale factor:

The scale factor, $\mathrm{k}$, represents the relationship between the scale drawing length and actual length.

Then, the square of this scale factor, ${\mathrm{k}}^2$, represents the relationship between the scale drawing area and the actual area.

Step-3: Match the scale drawing and the actual area to the correct scale.

When $\mathrm{k}$ is $1$ inch to $4$ feet, find ${\mathrm{k}}^2$ :

${\left(\frac{1}{4}\right)}^2=\frac{1}{16}$ [This matches with the $\left(\mathrm{C}\right)$]

When $\mathrm{k}$ is $1$ inch to $3$ feet, find ${\mathrm{k}}^2$ :

${\left(\frac{1}{3}\right)}^2=\frac{1}{9}$ [This matches with the $\left(\mathrm{A}\right)$]

When $\mathrm{k}$ is $1$ inch to $5$ feet, find ${\mathrm{k}}^2$:

${\left(\frac{1}{5}\right)}^2=\frac{1}{25}$ [This matches with the $\left(\mathrm{B}\right)$]

When $\mathrm{k}$ is $1$ inch to $2$ feet, find ${\mathrm{k}}^2$:

${\left(\frac{1}{2}\right)}^2=\frac{1}{4}$ [This matches with the $\left(\mathrm{D}\right)$]