Answer:
The area of the larger frame is 300 square inches
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
In this problem the ratio of the perimeters is 3:5
so
The scale factor is 3/5
step 2
Find the area of the larger frame
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 frame
y ----> the area of the larger frame
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{3}{5}[/tex]
[tex]x=108\ in^2[/tex]
substitute
[tex](\frac{3}{5})^{2}=\frac{108}{y}[/tex]
[tex]\frac{9}{25}=\frac{108}{y}[/tex]
solve for y
[tex]y=\frac{108}{9}(25)[/tex]
[tex]y=300\ in^2[/tex]
therefore
The area of the larger frame is 300 square inches
