Question

If the ratio of the side lengths of two similar rectangular

prisms is 3/5, what would be the ratio of their areas

Answer 1

Given:

Ratio of the side lengths of two similar rectangular prisms is
`(3)/(5)`.

To find:

The ratio of their areas.

Solution:

If two figures are similar then their areas are proportional to the squares of their corresponding sides.

`(A_1)/(A_2)=(s_1^2)/(s_2^2)`

`(A_1)/(A_2)=\left((s_1)/(s_2)\right)^2` ...(i)

Where,
`A_1,A_2` are areas and
`s_1,s_2` are corresponding sides.

It is given that ratio of the side lengths of two similar rectangular prisms is
`(3)/(5)`. It means,
`(s_1)/(s_2)=(3)/(5)`.

Using (i), we get

`(A_1)/(A_2)=\left((3)/(5)\right)^2`

`(A_1)/(A_2)=(3^2)/(5^2)`

`(A_1)/(A_2)=(9)/(25)`

Therefore, the ratio of their areas is
`(9)/(25)`. It is also written as 9:25.