Question

16

Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.​

Answer 1

The other individual who answered the question is correct, please give them 5 stars and a thanks.

Explanation:

To simplify and clarify, the answers are B, C, E

Answer 2

The options b) ,c) and e) are correct

The three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)
`((4)/(16))^2` , c)
`(12)/(192)` and e)
`((3)/(12))^2`

Explanation:

Given that a large rectangle has a length of 16 and width of 12.

A smaller rectangle has length of 4 and width of 3

To show the ratio of the area of the smaller rectangle to the area of the larger rectangle:

we know that "If two figures are similar, the the ratio of its areas is equal to the scale factor squared"

From the given scale factor is
`(1)/(4)`

Let z be the scale factor

Let x be the area of the smaller rectangle

Let y be the area of the large rectangle

`z^2=(x)/(y)`

Since scale factor is
`(1)/(4)` hence
`z=(1)/(4)`

we have
`z^2=((1)/(4))^2`

`=(1)/(16)`

∴
`z^2=(1)/(16)`

Now show that the ratio of the area of the smaller rectangle to the area of the larger rectangle with each options.

a)
`(4)/(16)`

`(4)/(16)=(1)/(4)`

Compare with
`(1)/(16)` we get,

`(1)/(4)\\eq (1)/(16)`

Hence it is not possible.

b)
`((4)/(16))^2`

`((4)/(16))^2=(16)/(256)`

`=(1)/(16)`

Compare with
`(1)/(16)` we get,

`(1)/(16)=(1)/(16)`

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.

c)
`(12)/(192)`

`=(1)/(16)`

Compare with
`(1)/(16)` we get,

`(1)/(16)=(1)/(16)`

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.

d)
`((4)/(12))^2`

`=(16)/(144)`

`=(1)/(9)`

Compare with
`(1)/(16)` we get,

`(1)/(9)\\eq (1)/(16)`

Hence it is not possible.

e)
`((3)/(12))^2`

`=(9)/(144)`

`=(1)/(16)`

Compare with
`(1)/(16)` we get,

`(1)/(16)=(1)/(16)`

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.

∴ options b) ,c) and e) are correct

The three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)
`((4)/(16))^2` , c)
`(12)/(192)` and e)
`((3)/(12))^2`