Answer to Question #158215 in Geometry for Janine Leodones

Question

The areas of two similar polygons are 72 sq. cm. and 50 sq. cm. A side of the

larger polygon is 4 cm. Find the corresponding side in the smaller polygon.

Answer 1

If the scale factor of the sides of two similar polygons is $k$, then the ratio of the areas is $k^2$ .

In our case $k^2=\frac{72}{50}=1.44.$

So, $k=\sqrt{1.44}=1.2.$

The corresponding side in the smaller polygon: $\frac{4}{1.2}=\frac{10}{3}$ cm.