The shipping box has a length of 30 inches and a height of 6 inches. How wide should the box be to fit the 36-inch bat? Show and explain your work.

width = 18.97 inches

Step-by-step explanation:

To find the smallest width of the box to fit the bat, we need to put the bat in the diagonal of the box.

The diagonal of the box is given by:

diagonal^2 = length^2 + width^2 + height^2

Then, using the diagonal = 36 inches, length = 30 inches and height = 6 inches, we have:

36^2 = 30^2 + width^2 + 6^2

1296 = 900 + width^2 + 36

width^2 = 360

width = 18.97 inches

details

step-by-step explanation:

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'.