One meter is equal to 100 centimeters, so the perimeter of 42 meters can be expressed as follows:

\(\displaystyle 42\) meters \(\displaystyle =42\times 100=4200\) centimeters

In a regular pentagon, all sides are equal in length. Divide the perimeter by 5 to get the length of each side:

\(\displaystyle 4200\div 5=840\) centimeters

The perimeter of a polygon is sum of the lengths of its sides. In this pentagon, three sides have the same length of 4 and two others have the same length of \(\displaystyle t\). So we can write:

\(\displaystyle Perimeter=4t-4=3\times 4+2\times t\)

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

\(\displaystyle 4t-4=12+2t\)

\(\displaystyle 4t-2t=12+4\)

\(\displaystyle 2t=16\)

\(\displaystyle t=8\)

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

\(\displaystyle x=\) length of one of those other three sides

Now we have:

\(\displaystyle Perimeter=40=2\times (3t+5)+3\times x\)

\(\displaystyle 40=6t+10+3x\)

\(\displaystyle 40-10-6t=3x\)

\(\displaystyle 30-6t=3x\)

\(\displaystyle 10-2t=x\)

So the length of each of those other three sides is \(\displaystyle 10-2t\)

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

\(\displaystyle Perimeter=2\times (t-1)+ 3\times (t+1)\)

\(\displaystyle =2t-2+3t+3\)

\(\displaystyle =5t+1\)

As each exterior angle of the pentagon is 72 degrees, each interior angle would be 

\(\displaystyle 180-72=108^{\circ}\)

That means all of the interior angles of the pentagon are identical, so we have a regular pentagon. 

The perimeter of a polygon is the sum of the lengths of its sides. So the perimeter of a regular pentagon is \(\displaystyle 5a\); where \(\displaystyle a\) is the length of a side.

So we get:

\(\displaystyle Perimeter=5a=5\times 4=20\) meters

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

\(\displaystyle Perimeter=4\left ( \frac{t^2}{4}-1 \right )+4\)

\(\displaystyle =4\times \frac{t^2}{4}-4\times 1+4\)

\(\displaystyle =t^2-4+4\)

\(\displaystyle =t^2\)

The perimeter of a square is four times its sidelength, so the perimeter of this square is

\(\displaystyle 4\left ( 2t - 17 \right ) = 4 \cdot 2t - 4 \cdot17 = 8t - 68\).

Perimeter of a square is four times the length of a side. The half-length of each side is equal to \(\displaystyle t+1\) that means the side length is equal to:

\(\displaystyle 2(t+1)=2t+2\)

So we can write:

\(\displaystyle Perimeter=4(2t+2)=8t+8\)

Perimeter of a square is four times the length of a side. The perimeter is known here and equal to 64 meters. So we can write:

\(\displaystyle Perimeter=64=4a\)

where \(\displaystyle a\) is the length of each side. So we have:

\(\displaystyle 64=4a\Rightarrow a=16\)

The length of each side is 16 meters. There are 100 centimeters in a meter. So we get:

\(\displaystyle a=16\times 100=1600\ cm\)

The perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a square, all four sides have the same length, so the perimeter is four times the length of a side. So we can write:

Perimeter of square = \(\displaystyle 4a\), where \(\displaystyle a\) is the length of a side.

In this problem:

\(\displaystyle a=4t+7\Rightarrow Perimeter = 4(4t+7)=16t+28\)