Question

the smaller rectangle is a 1/4 scale drawing of the original figure. Use the drop-down menus to show the missing dimensions of the scale figure.

Answer 1

Answer:

Part a) The length of the smaller rectangle is $6\ ft$

Part b) The width of the smaller rectangle is $5\ ft$

Part c) The area of the smaller rectangle is $30\ ft^{2}$

Step-by-step explanation:

Part a)

Find the length side of the smaller figure

we know that

The scale factor is equal to $\frac{1}{4}$

Remember that

The scale factor is equal to divide the measure of the smaller figure by the corresponding measure of the original figure

so

Let

x--------> the length of the smaller rectangle

y-------> the length of the original figure

z-----> scale factor

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

we have

$y=24\ ft$

$z=1/4$

substitute and solve for x

$(1/4)=\frac{x}{24}$

$x=24/4=6\ ft$

Part b)

Find the width side of the smaller figure

we know that

The scale factor is equal to $\frac{1}{4}$

Remember that

The scale factor is equal to divide the measure of the smaller figure by the corresponding measure of the original figure

so

Let

x--------> the width of the smaller rectangle

y-------> the width of the original figure

z-----> scale factor

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

we have

$y=20\ ft$

$z=1/4$

substitute and solve for x

$(1/4)=\frac{x}{20}$

$x=20/4=5\ ft$

Part c)

Find the area of the smaller figure

we know that

The scale factor is equal to $\frac{1}{4}$

Remember that

The scale factor squared is equal to divide the area of the smaller figure by the area of the original figure

so

Let

x--------> the area of the smaller rectangle

y-------> the area of the original figure

z-----> scale factor

so

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

we have

$y=480\ ft^{2}$

$z=1/4$

substitute and solve for x

$(1/4)^{2}=\frac{x}{480}$

$x=480/16=30\ ft^{2}$