Because of complexities that arise with square units, it is best to start a problem like this by changing all of your units into inches from the very beginning.  Thus, you know that the yard is $\displaystyle 40*12$ or $\displaystyle 480$ inches by $\displaystyle 25*12$ or $\displaystyle 300$ inches.

Thus, the area of the yard is $\displaystyle 300 * 480 = 144000$ $\displaystyle \textup{in}^{2}$

To find area, simply multiply length times width. Thus,

$\displaystyle A=lw=7\cdot6=42$

To solve, simply multiply width and length. Thus,

$\displaystyle A=w*l=4*12=48$

To solve, simply use the formula for the area of a rectangle. Thus,

$\displaystyle A=wl=5*8=40$

We know that the following represents the formula for the perimeter of a rectangle:

$\displaystyle P = 2l + 2w$  

In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:

$\displaystyle l = 2w$ 

Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.

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

$\displaystyle 24=6w$

$\displaystyle w=4$

We also know that the length is two times the width; therefore, we can write the following:

$\displaystyle l = 2w$

$\displaystyle l = 2\times4$

$\displaystyle l =8$

The area of a rectangle is found by using this formula:

$\displaystyle A = lw$

$\displaystyle A=8\times4$

$\displaystyle A=32$

The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.

1. Use Pythagorean Theorem with $\displaystyle a=14$ and $\displaystyle b=20$.

$\displaystyle a^{2}+b^{2}=c^{2}$

$\displaystyle 14^{2}+20^{2}=c^{2}$

2. Solve for $\displaystyle c$, the length of the diagonal:

$\displaystyle 14^{2}+20^{2}=c^{2}$

$\displaystyle 196+400=c^{2}$

$\displaystyle 596=c^{2}$

$\displaystyle c=24.41$

This rounds down to $\displaystyle 24.4$ because the hundredth's place ($\displaystyle 1$) is less than $\displaystyle 5$.

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 $\displaystyle 108$ $\displaystyle \textup{in}^{2}$.