To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides.  This number divided by 2 is the width. 

$\displaystyle 36-(12\cdot 2)=12$

$\displaystyle 12/2=6$

If we call the width of this rectangle $\displaystyle w$, then its length $\displaystyle L$ can be restated as$\displaystyle L=4\frac{1}{2}w$, or, equivalently, $\displaystyle L=4.5w$.

The perimeter can then be written as:

$\displaystyle P=2L+2w=2(4.5w)+2w$

Since the perimeter of the rectangle is 272 cm, we can set up the following equation:

$\displaystyle 2(4.5w)+2w=272$

$\displaystyle 9w+2w=272$

$\displaystyle 11w=272$

$\displaystyle w=\frac{272}{11}=24.7$

To find the width, we must take half of the length, which means we must divide the length by 2. Then we must take 2 more than that number, which means we must add 2 to the number. Combining these, we get:

w = ½ l + 2

The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2

We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8x. We then divide by 8 to get x = 48. 

Recall how to find the perimeter of a rectangle.

$\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\displaystyle \text{width}=\frac{14}{2}-5=7-5=2$

Recall how to find the perimeter of a rectangle.

$\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\displaystyle \text{width}=\frac{18}{2}-3=9-3=6$

Recall how to find the perimeter of a rectangle.

$\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\displaystyle \text{width}=\frac{20}{2}-9=10-9=1$

Recall how to find the perimeter of a rectangle.

$\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\displaystyle \text{width}=\frac{54}{2}-12=27-12=15$

Recall how to find the perimeter of a rectangle.

$\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\displaystyle \text{width}=\frac{22}{2}-5=11-5=6$