Answer:
The width of the smaller rectangle is 5 centimeters
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the smaller rectangle
y ----> the area of the larger rectangle
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=16\ cm^2\\y=100\ cm^2[/tex]
substitute
[tex]z^{2}=\frac{16}{100}[/tex]
square root both sides
[tex]z=\frac{4}{10}[/tex]
step 2
Find the width of the larger rectangle
we know that the area is equal to
[tex]A=LW[/tex]
we have
[tex]A=100\ cm^2\\L=8\ cm[/tex]
substitute
[tex]100=8W\\W=12.5\ cm[/tex]
step 3
Find the width of the smaller rectangle
To find out the width of the smaller rectangle, multiply the width of the larger rectangle by the scale factor
so
[tex]12.5(\frac{4}{10})=5\ cm[/tex]
