For this case we have:
Let:
l1, l2 the sides of the first frame
l1 ', l2' the sides of the second frame
We have as information the following:
[tex]\frac{l1}{l1'}=\frac{4}{5}[/tex], then [tex]l1=\frac{4}{5}*l1'[/tex]
[tex]\frac{l2}{l2'}=\frac{4}{5}[/tex], then [tex]l2=\frac{4}{5}*l2'[/tex]
On the other hand,
The area of table 1 is given by:
[tex]A1 = l1 * l2[/tex]
The area of table 2 is given by:
[tex]A2 = l1 '* l2'[/tex]
If we want to know the proportion of the areas, we have:
[tex]\frac{A1}{A2}=\frac{(l1*l2)}{(l1'*l2')}[/tex]
[tex]\frac{A1}{A2}=\frac{(\frac{4}{5}*l1')*(\frac{4}{5}*l2')}{(l1'*l2')}[/tex]
[tex]\frac{A1}{A2}=\frac{(\frac{16}{25})}{1}[/tex]
[tex]\frac{A1}{A2}=\frac{16}{25}[/tex]
Thus, the proportion of the areas is: [tex]\frac{A1}{A2}=\frac{16}{25}[/tex]
Answer:
[tex]\frac{A1}{A2}=\frac{16}{25}[/tex]