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

Part a) The length of the smaller rectangle is 6

Part b) The width of the smaller rectangle is 5

Part c) The area of the smaller rectangle is 30

Explanation:

Answer 2

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)`

Explanation:

Part a)

Find the length side of the smaller figure

we know that

The scale factor is equal to
`(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=(x)/(y)`

we have

`y=24\ ft`

`z=1/4`

substitute and solve for x

`(1/4)=(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
`(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=(x)/(y)`

we have

`y=20\ ft`

`z=1/4`

substitute and solve for x

`(1/4)=(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
`(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)=(x)/(y)`

we have

`y=480\ ft^(2)`

`z=1/4`

substitute and solve for x

`(1/4)^(2)=(x)/(480)`

`x=480/16=30\ ft^(2)`