Question

Two polygons are similar with the longest side of one 8 and the longest side of the other 10. Find the ratio of the areas.

Answer 1

The ratio of sides is, 8:10 = 4:5
squaring it yields, 16:25
the ratio of the area is 16:25

Answer 2

The ratio of the areas is
`(16)/(25)`

Explanation:

we know that

if two figures are similar, then the ratio of its areas is equal to the scale factor squared

and

the scale factor is equal to the ratio of its corresponding sides

Let

z------> the scale factor

In this problem we have

`z=(8)/(10)=(4)/(5)` -------> scale factor

The ratio of the areas is equal to

`z^(2)=((4)/(5))^(2)=(16)/(25)`