We know that:

\(\displaystyle Perimeter=2(a+b)\)

where:

\(\displaystyle a=Length \ of\ the\ rectangle\)

\(\displaystyle b= Width\ of\ the\ rectangle\)

So we can write:

\(\displaystyle 64=2(10x+6x)\Rightarrow 10x+6x=32\Rightarrow 16x=32\Rightarrow x=2\)

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

The sidelengths of the red polygon can now be added to find the perimeter:

\(\displaystyle 40 + 80 + 20 + 30 + 20 + 50 = 240\)

Start with the equation for the perimeter of a rectangle:

\(\displaystyle P=l+l+w+w=2l+2w\)

We know the perimeter is 72, the length is \(\displaystyle 6x\), and the width is \(\displaystyle 3x\). Plug these values into our equation.

\(\displaystyle 72=2(6x)+2(3x)\)

Multiply and combine like terms.

\(\displaystyle 72=12x+6x\)

\(\displaystyle 72=18x\)

Divide by 18 to isolate the variable.

\(\displaystyle \frac{72}{18}=x\)

Simplify the fraction by removing the common factor.

\(\displaystyle \frac{72}{18}=\frac{72\div18}{18\div18}=\frac{4}{1}=4\)

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

\(\displaystyle 40 + 80 + 40 + 80 = 240\).

The smaller rectangle has perimeter

\(\displaystyle 20 + 30 + 20 + 30 = 100\).

The ratio is

\(\displaystyle \frac{240}{100} = \frac{240 \div 20 }{100\div 20 } = \frac{12}{5}\); that is, 12 to 5.

The formula for the perimeter of a rectangle is \(\displaystyle \dpi{100} Perimeter=2l+2w\).

Plug in our given values to solve:

\(\displaystyle \dpi{100} Perimeter = 2(20)+2(3)\)

\(\displaystyle \dpi{100} Perimeter = 20+6\)

\(\displaystyle \dpi{100} Perimeter = 26\)

The area of a rectangle is found by multiplying the length times the width.  The question tells you the width is \(\displaystyle 5\) and the area is \(\displaystyle 40\).  

Thus the length is 8. \(\displaystyle \left ( 40 \div5\right)\).

To find the perimeter you add up all of the sides.  

\(\displaystyle length+length+width+width=perimeter\)

 \(\displaystyle 8 + 8 + 5 + 5 = 26\)

The perimeter of a rectangle is represented by the following formula, in which W represents width and L represents length:

\(\displaystyle 2W+2L= Perimeter\)

Given that the width is \(\displaystyle 2\) inches and that the perimeter is \(\displaystyle 14\) inches, the following applies:

\(\displaystyle 2\cdot 2+2L=14\)

\(\displaystyle 4+2L=14\)

Next, subtract \(\displaystyle 4\) from each side.

\(\displaystyle 2L=10\)

Now, divide each side by \(\displaystyle 2\).

This gives us

\(\displaystyle L=5\)

Since each side is a whole number, first find the whole number factors of \(\displaystyle 24\). They are \(\displaystyle 3\) and \(\displaystyle 8\), \(\displaystyle 12\) and \(\displaystyle 2\), \(\displaystyle 24\) and \(\displaystyle 1\), and \(\displaystyle 6\) and \(\displaystyle 4\). These sidelengths correspond to perimeters of \(\displaystyle 22\), \(\displaystyle 28\), \(\displaystyle 50\), and \(\displaystyle 20\), respectively. Thus, \(\displaystyle 23\) is answer. 

The perimeter of the rectangle is \(\displaystyle 8 + 3 + 8 + 3 = 22\) yards. To convert this to centimeters, multiply by the given conversion factor:

\(\displaystyle 91.44 \times 22 = 2,011.68\) centimeters.

The perimeter of a rectangle, or any shape, is the distance around the outside. You add up the length of each side to find this number. The coordinates of the points are \(\displaystyle (-3,8)(5,8)(5,-2)(-3,-2)\). You need to find the distance between each point. The short side is \(\displaystyle 8\) units, and the longer side is \(\displaystyle 10\) units. 

\(\displaystyle (8\times2)+(10\times2)=16+20=36\)