Question

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

Answer 1

Answer:

4/16

12/192

3/12 squared

explanation:

i took the test and have all a's

Answer 2

Answer:

$(\frac{4}{16})^2$

$\frac{12}{192}$

$(\frac{3}{12})^2$

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

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

we have

$z=\frac{1}{4}$

substitute

$z^2=(\frac{1}{4})^2 =\frac{1}{16}$

Verify each option

a) we have

$\frac{4}{16}$

Compare with  $\frac{1}{16}$

so

$\frac{4}{16} \neq \frac{1}{16}$

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

b) we have

$(\frac{4}{16})^2=\frac{16}{256}=\frac{1}{16}$

Compare with  $\frac{1}{16}$

so

$\frac{1}{16} = \frac{1}{16}$

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

c) we have

$\frac{12}{192}=\frac{1}{16}$

Compare with  $\frac{1}{16}$

so

$\frac{1}{16} = \frac{1}{16}$

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

d) we have

$(\frac{4}{12})^2=\frac{16}{144}=\frac{1}{9}$

Compare with  $\frac{1}{16}$

so

$\frac{1}{9} \neq \frac{1}{16}$

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

e) we have

$(\frac{3}{12})^2=\frac{9}{144}=\frac{1}{16}$

Compare with  $\frac{1}{16}$

so

$\frac{1}{16} = \frac{1}{16}$

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