Answer:
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
