Hector needs 84 feet of fencing to enclose his rectangular gardenThe length of his garden is 12 feet less than twice its widthWhat is the width of his garden?

The width of his garden is 18 feet.

Step-by-step explanation:

Let the length of Hector's rectangular garden is a feet and width is b feet.

So, by the given condition, we can write that  

2(a + b) = 84

⇒ a + b = 42 (1)

Again, the length of his garden is 12 feet less than twice its width.

So, a = 2b - 12 (2)

Now, solving equations (1) and (2) we get,

(2b - 12) + b = 42

⇒ 3b = 54

⇒ b = 18 feet.

Now, from equation (1) we get,

a = 42 - b = 42 - 18 = 24 feet.

Therefore, the width of his garden is 18 feet. (Answer)

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.