Question

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?

Answer 1

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:

$\frac{l1}{l1'}=\frac{4}{5}$, then $l1=\frac{4}{5}*l1'$

$\frac{l2}{l2'}=\frac{4}{5}$, then $l2=\frac{4}{5}*l2'$

On the other hand,

The area of table 1 is given by:

$A1 = l1 * l2$

The area of table 2 is given by:

$A2 = l1 '* l2'$

If we want to know the proportion of the areas, we have:

$\frac{A1}{A2}=\frac{(l1*l2)}{(l1'*l2')}$

$\frac{A1}{A2}=\frac{(\frac{4}{5}*l1')*(\frac{4}{5}*l2')}{(l1'*l2')}$

$\frac{A1}{A2}=\frac{(\frac{16}{25})}{1}$

$\frac{A1}{A2}=\frac{16}{25}$

Thus, the proportion of the areas is: $\frac{A1}{A2}=\frac{16}{25}$

Answer:

$\frac{A1}{A2}=\frac{16}{25}$