A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:

\(\displaystyle a^2+b^2=c^2\) where a and b are the sides of the rectangle and c is the length of the diagonal. 

\(\displaystyle \sqrt{4^2+16^2}=\sqrt{185}=c\)

Notice that this problem could be represented as follows:

This means that you can find the distance of the wire merely by using the Pythagorean theorem:

\(\displaystyle 6^2+2^2=c^2\)

Solving for \(\displaystyle c\), you get:

\(\displaystyle c^2 = 36+4\)

\(\displaystyle c^2 = 40\)

Thus, \(\displaystyle c=\sqrt{40}\)

Using your calculator, multiply this by \(\displaystyle 15250\).  This gives you approximately \(\displaystyle 96449.47\) dollars in expenses.

You could draw this rectangle as follows:

Solving for the diagonal merely requires using the Pythagorean theorem. Thus, you know:

\(\displaystyle 3^2+12^2=c^2\) or 

\(\displaystyle 9+144=c^2\)

\(\displaystyle c^2=153\), meaning that \(\displaystyle c=\sqrt{153}\)

This is approximately \(\displaystyle 12.36931687685298...\) Thus, the answer is \(\displaystyle 12.37\).

Based on the description offered in the question, you know that your rectangle must look something like this:

Using the Pythagorean theorem, you can solve for the unknown side \(\displaystyle x\):

\(\displaystyle 9^2+x^2=15^2\)

\(\displaystyle 81+x^2=225\)

\(\displaystyle x^2=144\)

Thus, \(\displaystyle x\) is \(\displaystyle 12\).  This means that the area is \(\displaystyle 9*12\) or \(\displaystyle 108\) \(\displaystyle \textup{in}^{2}\).

Finding the diagonal of a rectangle is essentially a problem with triangles. If we set up a right triangle with legs 24 in. and 36 in., and set \(\displaystyle d\) to be the diagonal (the hypotenuse), we can use the Pythagorean Theorem to solve for \(\displaystyle d\):

\(\displaystyle {} 24^2+36^2=d^2\)

\(\displaystyle {} d=\sqrt{1872}\)

This comes out to be about 43.3 in.

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. 

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.