Arectangle has a long side of length 8.5 cm.

its perimeter is 24 cm.

work out the length of the shorter sides.

The length of the shorter side is 3.5 cm.

length = 8.5 cm

perimeter = 24 cm

perimeter of a rectangle = 2(l + w)

Therefore,

24 = 2(8.5 + w)

24 = 17 + 2w

subtract 17 from both sides

24 - 17 = 2w

7 = 2w

w = 7 / 2

w = 3.5 cm

Therefore, the length of the shorter side is 3.5 cm

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hope you understand. this, I think, is the right 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'.