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

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

we have

substitute

Verify each option

a) we have

Compare with  

so

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

b) we have

Compare with  

so

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

c) we have

Compare with  

so

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

d) we have

Compare with  

so

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

e) we have

Compare with  

so

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

4/16

12/192

3/12 squared

explanation:

i took the test and have all a's