Mason has 108 feet of material to build a fence around a rectangular pool on his property. if the width of the fence must be 6 feet, what is the length of the fence in yards if he uses all 108 feet of material? a. 48 yards b. 16 yards c. 96 yards d. 32 yards

Option A (48 yards).

Step-by-step explanation:

The perimeter of any shape other than the ellipse is given by:

Perimeter = Sum of all sides.

Since there are two pairs of lines and both lines in the pair are congruent in each other in a rectangle, the formula can be updated as:

Perimeter of a rectangle = 2L + 2W; where L is the length and W is the width.

The perimeter of the fence around the rectangular pool is 108 feet and the width of the pool is 6 feet. The length can be calculated by plugging in the values in the above equation:

108 = 2L + 2(6).

2L = 108 - 12.

L = 96/2.

L = 48 feet.

So Option A is the correct 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'.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .