A side of a regular hexagon is three less than twice the length of a side of a regular decagon.If the perimeter of the hexagon equals the perimeter...

The regular hexagon has 6 equal sides and the regular
decagon has 10 equal sides.

We'll note as x = side of the
regular decagon

According to the enunciation, the side of
hexagon is 2x - 3.

We'll note the perimeter of decagon as
P1 and the perimeter of hexagon as P2.

We'll also note the
sides of the decagon as d1,d2... and the sides of the hexagon as
h1,h2...

We'll calculate the perimeter of
decagon:

P1 = d1 + d2 + ... +
d10

Since d1 = d2 = ... = d10 =
x

P1 = 10x

We'll calculate the
perimeter of hexagon:

P2 = h1 + h2 + ... +
h6

Since h1 = h2 = ... = h6 = 2x -
3

P2 = 6(2x - 3)

We know, from
enunciation, that the perimeters are equals:

P1 =
P2

10x = 6(2x-3)

We'll remove
the brackets:

10x = 12x -
18

We'll subtract 12x - 18 both
sides:

10x - 12x + 18 =
0

We'll combine like
terms:

-2x + 18 = 0

We'll
subtract 18 both sides:

-2x =
-18

We'll divide by -2:

x =
9

The side of the regular hexagon
is:

h = 2x -
3

h = 2*9 - 3

h = 18 -
3

h =
15