Question

The scale drawing of a rectangular room will be enlarged by a scale factor of 4 to create the actual room. The actual area of the room will be 150 square feet. Which expression finds the area of the scale drawing?

Answer 1

Answer:

The expression is equal to $\frac{150}{4^{2}}$

The area of the scale drawing is $9.375\ ft^{2}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

let

z------> the scale factor

x------> the area of the actual room

y-----> the area of the scale drawing

so

$z^{2}=\frac{x}{y}$

we have

$z=4$

$x=150\ ft^{2}$

substitute and solve for y

$4^{2}=\frac{150}{y}$

$y=\frac{150}{4^{2}}=9.375\ ft^{2}$