If each side of a square is increased by 6, the area is multiplied by 16

The original side length is 2. The area of the original square is 4.

This means the new side length, x+6, would be 8. The area of the new square is 64.

Step-by-step explanation:

If you want to know what the length of the side is, here is how you solve it:

x is the side length

therefore, is the area

if x+6 becomes the length and the area of this is 16

then we can say that

we can expand this to become

which becomes

If we factor it, we get

because length cannot be a negative number, the only option for the original side length is 2. The area of the original square is 4.

This means the new side length, x+6, would be 8. The area of the new square is 64.

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'.