Answer:
The area of rectangle A'B'C'D' is 32 square feet
Step-by-step explanation:
step 1
Find out the scale factor
we know that
If two figures are similar, the the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z ----> the scale factor
x -----> width of rectangle A'B'C'D'
y -----> width of rectangle ABCD
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=8\ ft\\y=12\ ft[/tex]
substitute the values
[tex]z=\frac{8}{12}[/tex]
Simplify
[tex]z=\frac{2}{3}[/tex]
step 2
Find out the area of rectangle A'B'C'D'
we know that
If two figures are similar, the the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x -----> area of rectangle A'B'C'D'
y -----> area of rectangle ABCD
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]y=72\ ft^2[/tex]
[tex]z=\frac{2}{3}[/tex]
substitute the values
[tex](\frac{2}{3})^2=\frac{x}{72}[/tex]
[tex]\frac{4}{9}=\frac{x}{72}[/tex]
[tex]x=\frac{4}{9}(72)\\\\ x=32\ ft^2[/tex]
therefore
The area of rectangle A'B'C'D' is 32 square feet
