Two similar polygons have areas of 4 square inches and 64 square inches.The ratio of a pair of corresponding sides is .The ratio of

Two similar polygons have areas of 4 square inches and 64 square inches. The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .

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  1. Option A is correct

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

    Step-by-step 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;

    [tex]\frac{4}{64}=\frac{a^2}{b^2}[/tex]

    ⇒[tex]\frac{1}{16} = (\frac{a}{b})^2[/tex]

    ⇒[tex]\sqrt{\frac{1}{16}} =\frac{a}{b}[/tex]

    ⇒[tex]\frac{1}{4} = \frac{a}{b}[/tex]

    or

    [tex]\frac{a}{b} = \frac{1}{4}[/tex]

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

  2. 4

    Step-by-step explanation:

    The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.

  3. That is true

    Step-by-step explanation:

    The ratio is a one-to-one measure, literally a ratio of the sides in reduced form.  The area is that one-to-one ratio squared.

    Our numbers are already squared, so in order to find the one-to-one we have to take the square roots of both of them.  

    [tex]\frac{\sqrt{4} }{\sqrt{64} } =\frac{2}{8} =\frac{1}{4}[/tex].

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