A side of a regular hexagon is three less than twice the len

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 of decagon find a side of the hexagon.

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