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:

`(l1)/(l1')=(4)/(5)`, then
`l1=(4)/(5)*l1'`

`(l2)/(l2')=(4)/(5)`, then
`l2=(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:

`(A1)/(A2)=((l1*l2))/((l1'*l2'))`

`(A1)/(A2)=(((4)/(5)*l1')*((4)/(5)*l2'))/((l1'*l2'))`

`(A1)/(A2)=(((16)/(25)))/(1)`

`(A1)/(A2)=(16)/(25)`

Thus, the proportion of the areas is:
`(A1)/(A2)=(16)/(25)`

Answer:

`(A1)/(A2)=(16)/(25)`