Question

The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon with two sides of length 3.

Answer 1

The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

`(a)/(3)=(3)/(2)` multiply both sides by 3

`a=(3)/(2)=4.5`

`(b)/(4)=(3)/(2)` multiply both sides by 4

`b=(3)/(2)\cdot4=6`

`(c)/(6)=(3)/(2)` multiply both sides by 6

`c=(3)/(2)\cdot6=9`

`(d)/(7)=(3)/(2)` multiply both sides by 7

`d=(21)/(2)=10.5`

The perimeter:

`P=4.5+6+9+10.5=30`