The sidelength of the garden, in feet, is  feet less than that of the entire lot, or 

;

The perimeter, in feet, of the garden is four times this:

You have a pentagonal-shaped lot with side lengths of 120ft,30ft, 55ft, 60 ft, and a longest side which is triple the length of the third longest side. What is the perimeter around the lot?

So, we have a five-sided lot and are given 4 sides, and the means to find the 5th.

The longest side is triple the length of the third longest side:

The third longest side is 60 feet, therefore, the longest side is 180 ft

Find the perimeter by adding up all the sides:

So our answer is 445 feet

The circumference of a circle is denoted by the formula  where r is the radius of the circle. The problem gives us the diameter of the circle which must be used to find the radius.

Plug the radius into the formula for the area of a circle

The perimeter of a triangle is the sum of all three sides of the triangle.

Add all the side lengths.

Expand the terms in the bracket and remove all parentheses.

Combine like-terms.

The answer is:  

A square can be a rectangle, but a rectangle cannot be a square.   We cannot assume that the width is known given just the length of the rectangle.  There is not enough information to determine the perimeter just by the side length alone.

The answer is:  

The perimeter of the hexagonal track is one half of a mile. One mile is equal to 5,280 feet, so one half of a mile is equal to 

Each of the six congruent sides measures one sixth of this, or

The hexagonal track is recreated below, with its six radii constructed - the center is called .

The radii divide the hexagon into six equilateral triangles, so each of the radii has length equal to one side of the hexagon. Selena's path takes her along , , , , and  - a path equivalent in distance to five sides of the hexagon. Therefore, Selena runs a distance of

Determine the length of the square by using the given area.

Substitute the area.

There are four congruent sides in a square, which means the perimeter is four times the side.

The answer is:  

Use the Pythagorean Theorem to determine the hypotenuse.

Substitute the base and height.

Square root both sides to find the hypotenuse.

Add the sides to determine the perimeter.

The answer is:  

If a particle accelerator has a circumference of , what is its radius?

Begin with the formula for the circumference of a circle:

Now, we know the circumference, so just plug in and solve for r.

Divide both sides by 2 pi to get out answer:

If a particle accelerator has a circumference of , what is its radius?

Begin with the formula for circumference of a circle:

Now, we can see that 2r is really the same as d, right? Our radius will always be half the length of the diameter.

So, we can rewrite the above equation as:

Now, plug in our circumference and solve for d:

Divide both sides by pi to get:

So our answer is 18.5 miles