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.

$\dfrac{a}{3}=\dfrac{3}{2}$     multiply both sides by 3

$a=\dfrac{3}{2}=4.5$

$\dfrac{b}{4}=\dfrac{3}{2}$   multiply both sides by 4

$b=\dfrac{3}{2}\cdot4=6$

$\dfrac{c}{6}=\dfrac{3}{2}$     multiply both sides by 6

$c=\dfrac{3}{2}\cdot6=9$

$\dfrac{d}{7}=\dfrac{3}{2}$    multiply both sides by 7

$d=\dfrac{21}{2}=10.5$

The perimeter:

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