Question

If two polygons are similar with the lengths of their corresponding sides in the ratio of a/b , then the ratio of their areas is _____.

Answer 1

Answer:

The ratio of their areas is $\frac{a^{2}}{b^{2}}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

In this problem the scale factor is equal to

$z=\frac{a}{b}$

therefore

the scale factor squared is equal to

$z^{2} =\frac{a^{2}}{b^{2}}$