2 hexagons are similar. if the ratio of their perimeters is 8:5, and a side of the larger hexagon measures 32 cm. find the length of the corresponding side of the smaller hexagon

20 cm

Step-by-step explanation:

An hexagon has 6 equal sides therefore its perimeter is obtained by summing up all the values of the 6 sides

For the bigger hexagon, the perimeter = 32 + 32 + 32 + 32 + 32 + 32

or 6 * 32

= 192 cm

Next, we'll calculate the perimeter of the smaller hexagon

Since their perimeters are in the ratio 8: 5

Let x represent the perimeter of the smaller hexagon

This gives;

8 : 5 = 192 : x

change to fraction

8/5 = 192 / x

cross multiply

8x = 192*5

8x = 960

Divide both sides by the coefficient if x which is 8

x = 120 cm

Since all sides of an hexagon are equal, we'll simple divide the value of the perimeter by the number of sides of the hexagon

120/6

20 cm

Therefore, the length of the corresponding smaller hexagon is 20 cm