One meter is equal to 1,000 millimeters, so the perimeter of 9 meters can be expressed as:

9 meters = \(\displaystyle 9 \times 1,000 = 9,000\) millimeters.

Since the six sides of a regular hexagon are congruent, divide by 6:

\(\displaystyle 9,000 \div 6 = 1,500\) millimeters.

The perimeter of a polygon is the sum of the lengths of its sides. Let:

\(\displaystyle x=\) Length of one of those other two sides

Now we can set up an equation and solve it for \(\displaystyle x\) in terms of \(\displaystyle t\):

\(\displaystyle 2x+4(t+1)=60\)

\(\displaystyle \Rightarrow 2x+4t+4=60\)

\(\displaystyle \Rightarrow 2x=60-4-4t\)

\(\displaystyle \Rightarrow 2x=56-4t\)

\(\displaystyle \Rightarrow x=28-2t\)

The perimeter of a polygon is the sum of the lengths of its sides. So we can write:

\(\displaystyle Perimeter=2\left [ t+(t+1)+(t-1) \right ]=2(3t)=6t\)

As the six sides of a regular hexagon are congruent, we can write:

\(\displaystyle Perimeter=6a=15\Rightarrow a=2.5\) feet; \(\displaystyle a\) is the length of each side.

One feet is equal to 12 inches, so we can write:

\(\displaystyle a=2.5\times 12=30\) inches

Since each interior angle of a hexagon is 120 degrees, we have a regular hexagon with identical side lengths. And we know that the perimeter of a polygon is the sum of the lengths of its sides. So we can write:

\(\displaystyle Perimeter=6a=120\Rightarrow a=20\) inches

The perimeter of a polygon is the sum of the lengths of its sides. Since three sides are congruent with the length of \(\displaystyle 2t+3\) and the rest of the sides have the length of \(\displaystyle 2t-7\) we can write:

\(\displaystyle Perimeter=3(2t+3)+3(2t-7)=48\)

Now we should solve the equation for \(\displaystyle t\):

\(\displaystyle 6t+9+6t-21=48\Rightarrow 12t-12=48\Rightarrow 12t=60\Rightarrow t=5\)

A regular polygon has all of its sides the same length. The pentagon has perimeter \(\displaystyle 5 \times 12 \textrm{ in } = 60 \textrm{ in }\); the hexagon has perimeter \(\displaystyle 6 \times 10 \textrm{ in } = 60 \textrm{ in }\). The sum of the perimeters is \(\displaystyle 60 \textrm{ in } + 60 \textrm{ in }= 120 \textrm{ in }\), which is the perimeter of the octagon; each side of the octagon has length \(\displaystyle 120 \textrm{ in } \div 8 = 15 \textrm{ in }\).

A hexagon has six sides.  The perimeter of a hexagon is:

\(\displaystyle P=6s\)

Substitute the side length.

\(\displaystyle P=6s=6(6a+b)=36a+6b\)

The perimeter of a polygon is the sum of the lengths of its sides. If we let \(\displaystyle X\) be the length of one of those other two sides, we can set up this equation and solve for \(\displaystyle X\):

\(\displaystyle 2X + 3 (2t-5) = 54\)

\(\displaystyle 2X + 3 \cdot 2t-3 \cdot 5 = 54\)

\(\displaystyle 2X +6t-15 = 54\)

\(\displaystyle 2X +6t-15 + 15 - 6t= 54+ 15 - 6t\)

\(\displaystyle 2X =69- 6t\)

\(\displaystyle 2X \div 2 =\left ( 69- 6t \right )\div 2\)

\(\displaystyle X =\frac{- 6t+ 69 }{2}\)

One meter is equal to 1,000 millimeters, so the perimeter of 7 meters can be expressed as:

7 meters = \(\displaystyle 7 \times 1,000 = 7,000\) millimeters.

Since the five sides of a regular pentagon are congruent, divide by 5:

\(\displaystyle 7,000 \div 5 = 1,400\) millimeters.