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.
[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex] multiply both sides by 3
[tex]a=\dfrac{3}{2}=4.5[/tex]
[tex]\dfrac{b}{4}=\dfrac{3}{2} [/tex] multiply both sides by 4
[tex]b=\dfrac{3}{2}\cdot4=6[/tex]
[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex] multiply both sides by 6
[tex]c=\dfrac{3}{2}\cdot6=9[/tex]
[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex] multiply both sides by 7
[tex]d=\dfrac{21}{2}=10.5[/tex]
The perimeter:
[tex]P=4.5+6+9+10.5=30[/tex]
