You by 2 picture frames that are similar the ratio of the corresponding side lengths is 4 : 5. what is the ratio of the areas?

Respuesta :

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]