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

The options b) ,c) and e) are correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b) , c) and e)

Step-by-step 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

Let z be the scale factor

Let x be the area of the smaller rectangle

Let y be the area of the large rectangle

Since scale factor is hence  

we have

∴

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

a)

Compare with   we get,

Hence it is not possible.

b)

Compare with   we get,

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

c)

Compare with   we get,

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

d)

Compare with   we get,

Hence it is not possible.

e)

Compare with   we get,

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 correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b) , c) and e)

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