The perimeter of a square is four times its sidelength, so the perimeter of this square is

$\displaystyle 4\left ( 2t - 17 \right ) = 4 \cdot 2t - 4 \cdot17 = 8t - 68$.

Perimeter of a square is four times the length of a side. The half-length of each side is equal to $\displaystyle t+1$ that means the side length is equal to:

$\displaystyle 2(t+1)=2t+2$

So we can write:

$\displaystyle Perimeter=4(2t+2)=8t+8$

Perimeter of a square is four times the length of a side. The perimeter is known here and equal to 64 meters. So we can write:

$\displaystyle Perimeter=64=4a$

where $\displaystyle a$ is the length of each side. So we have:

$\displaystyle 64=4a\Rightarrow a=16$

The length of each side is 16 meters. There are 100 centimeters in a meter. So we get:

$\displaystyle a=16\times 100=1600\ cm$

The perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a square, all four sides have the same length, so the perimeter is four times the length of a side. So we can write:

Perimeter of square = $\displaystyle 4a$, where $\displaystyle a$ is the length of a side.

In this problem:

$\displaystyle a=4t+7\Rightarrow Perimeter = 4(4t+7)=16t+28$

To find the perimter of a square, multiply the side length by 4.

$\displaystyle 4(x-8)=4x-32$

Since the diagonal of a squre is also the hypotenuse of a right triangle whose legs are the sides of the square, use the Pythagorean Theorem to find out the lengths of the sides of the square.

$\displaystyle (4\sqrt2)^2=\text{side}^2+\text{side}^2$

$\displaystyle 32=2(\text{side}^2)$

$\displaystyle 16=\text{side}^2$

$\displaystyle 4=\text{side}$

Now, multiply the side length by 4 to find the perimter.

$\displaystyle 4\times4=16$

To figure out the perimeter, we need to first find the length of 1 side of the square. 

Find the length of a side of the square using the information given about the area.

$\displaystyle \text{Area}=(\text{side length})^2$

$\displaystyle 400\:m^2=(\text{side length})^2$

$\displaystyle \text{side length}=20\: m$

Now, multiply the side length by 4.

$\displaystyle 20\times4=80\:m$

The diagonal of a square is also the hypotenuse of a triangle whose legs are two sides of the square. Using that information, we can find the length of each side of the square.

$\displaystyle (6\sqrt{2})^2=(\text{side})^2+(\text{side})^2$

$\displaystyle 72=2(\text{side})^2$

$\displaystyle 36=\text{side}^2$

$\displaystyle 6\: cm=\text{side}$

Now, multiply the side length by 4 to find the perimeter.

$\displaystyle 6\:cm\times4\:cm=24\:cm^2$

A square with diagonal 600 feet will have as its sidelength 

$\displaystyle 600 \div \sqrt {2 } \approx 600 \div 1.4 = 429$ feet.

If Corinne runs the entire perimeter of the square three times, and then runs on to Point B, she will run this distance a total of about $\displaystyle 14 \frac{3}{4}$ times. This is a total of

$\displaystyle 429 \times 14 \frac{3}{4} \approx 6,328$ feet.

Divide by 5,280 to convert to miles:

$\displaystyle 6,328 \div 5,280 \approx 1.2$

The closest response is 1 mile.

A square with diagonal 400 feet will have as its sidelength 

$\displaystyle 400 \div \sqrt {2 } \approx 400 \div 1.414 = 283$ feet.

Julia wants to run one mile, or 5,280 feet; this will be

$\displaystyle 5,280 \div 283 \approx 18.7$ sidelengths.

Julia will run around the track four times, then another 2 sidelengths. She will then run seven-tenths of the length of the "bottom" side, ending up at point D.