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. 

The perimeter of a figure is the sum of the lengths of all of its sides. The perimeter of this figure is √27 + 2√3 + √27 + 2√3. But, √27 = √9√3 = 3√3 . Now all of the sides have the same number underneath of the radical symbol (i.e. the same radicand) and so the coefficients of each radical can be added together. The result is that the perimeter is equal to 10√3.

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.

Area of rectangle:  A = lw

Perimeter of rectangle:  P = 2l + 2w

w = width and l = w + 3

So A = w(w + 3) = 40 therefore w² + 3w – 40 = 0

Factor the quadratic equation and set each factor to 0 and solve.

w² + 3w – 40 = (w – 5)(w + 8) = 0 so w = 5 or w = -8. 

The only answer that makes sense is 5.  You cannot have a negative value for a length.

Therefore, w = 5 and l = 8, so P = 2l + 2w = 2(8) + 2(5) = 26 in.

Leaving the width to be x, the length is 4x. The total perimeter is 4x + 4x + x + x = 10x.

We divide 25 by 10 to get 2.5, the time required to walk the width.  Therefore the time required to walk the length is (4)(2.5) = 10.

The area of a rectangle is the width times the height, and we are told that in this rectangle the width is two times the height.

Therefore, .

Plug in the value of the area:

Solve for  to find a width of 4 inches. Using our formula above, the height must be 8 inches.  We then add all the sides of the rectangle together to find the perimeter:

Let l be the length of the garden and w be the width. 

By the specifications of the problem, l = 2w-3.

Plug this in for length in the area formula:

A = l  x w = (2w - 3) x w = 9

Solve for the width:

2w²- 3w - 9 =0 

(2w + 3)(w - 3) = 0

w is either 3 or -3/2, but we can't have a negative width, so w = 3.

If w = 3, then length = 2(3) - 3 = 3.

Now plug the width and length into the formula for perimeter:

P = 2 l + 2w = 2(3) + 2(3) = 12

Based on the information provided, you know that the rectangle's area could be represented as:

, where  is the unknown side of the rectangle. Solving for , you get  . 

Now, remember that your perimeter is just the sum of all the sides. This is:

For our data, this is:

Begin by computing the length of the other side of the yard.  Based on the data that you have, you know that:

, where  is the other side in yards. Solving for  is:

Now, this means that our yard's dimensions in feet are:

The perimeter will be . For our data, this is:

Based on this data, you know that the person purchased a total of  or   of fence. Based on all of the data you have, you can write the two equations:

Solve the first equation for :

Now substitute this into the first equation:

Since this is a quadratic equation, isolate everything to one side:

This is a bit tricky to factor, but it comes out as:

This means that the larger dimension is  .