Question

Two similar polygons have areas of 4 square inches and 64 square inches.

The ratio of a pair of corresponding sides is 1/4
The ratio of a pair of corresponding sides is 1/2
The ratio of a pair of corresponding sides is 1/8
The ratio of a pair of corresponding sides is 1/16

Answer 1

The ratio of a pair of corresponding sides of 1/16.

Answer 2

Option A is correct

The ratio of a pair of corresponding sides is 1/4

Explanation:

Definition:

If two polygons are similar, then

the area of similar figure is the square of the ratio of its corresponding sides.

As per the statement:

Two similar polygons have areas of 4 square inches and 64 square inches

Let the corresponding sides of the polynomials are a and b.

then by definition we have;

`(4)/(64)=(a^2)/(b^2)`

⇒
`(1)/(16) = ((a)/(b))^2`

⇒
`\sqrt{(1)/(16)} =(a)/(b)`

⇒
`(1)/(4) = (a)/(b)`

or

`(a)/(b) = (1)/(4)`

Therefore, The ratio of a pair of corresponding sides is 1/4.