Question

A rectangle is reduced by a scale factor of One-fourth.

A large rectangle has a length of 16 and width of 12. A smaller rectangle has length of 4 and width of 3.


Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.

a. 4 / 16

b. 4 / 16 squared

c. 12 / 192

d. 4 squared / 12 squared

e. 3 / 12 squared

Answer 1

4/16

12/192

3/12 squared

Step-by-step explanation:

i took the test and have all a's

Answer 2

`((4)/(16))^2`

`(12)/(192)`

`((3)/(12))^2`

Step-by-step explanation:

we know that

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

In this problem

The scale factor is 1/4

Let

z ---> the scale factor

x ---> the area of the smaller rectangle

y ---> the area of the large rectangle

so

`z^2=(x)/(y)`

we have

`z=(1)/(4)`

substitute

`z^2=((1)/(4))^2 =(1)/(16)`

Verify each option

a) we have

`(4)/(16)`

Compare with
`(1)/(16)`

so

`(4)/(16) \\eq (1)/(16)`

This option no show the ratio of the area of the smaller rectangle to the area of the larger rectangle

b) we have

`((4)/(16))^2=(16)/(256)=(1)/(16)`

Compare with
`(1)/(16)`

so

`(1)/(16) = (1)/(16)`

This option show the ratio of the area of the smaller rectangle to the area of the larger rectangle

c) we have

`(12)/(192)=(1)/(16)`

Compare with
`(1)/(16)`

so

`(1)/(16) = (1)/(16)`

This option show the ratio of the area of the smaller rectangle to the area of the larger rectangle

d) we have

`((4)/(12))^2=(16)/(144)=(1)/(9)`

Compare with
`(1)/(16)`

so

`(1)/(9) \\eq (1)/(16)`

This option no show the ratio of the area of the smaller rectangle to the area of the larger rectangle

e) we have

`((3)/(12))^2=(9)/(144)=(1)/(16)`

Compare with
`(1)/(16)`

so

`(1)/(16) = (1)/(16)`

This option show the ratio of the area of the smaller rectangle to the area of the larger rectangle