Final answer:
To find the length of the shorter side, first express the perimeter as 2(x + 2x - 2) = 50, then solve for x which is 9. The shorter side is then calculated using the expression 2x - 2 to get 16 units.
Step-by-step explanation:
To find the length of the shorter side of the rectangle when the perimeter is 50 units and one side is x and the other is 2x - 2, we first need to express the perimeter P in terms of x using the formula for the perimeter of a rectangle: P = 2(length + width). Here, the length can be x and the width can be 2x - 2. So the perimeter is:
P = 2(x + 2x - 2)
This simplifies to:
50 = 2(3x - 2)
50 = 6x - 4
When we solve for x, we get:
54 = 6x
9 = x
Since x is the length of one side, it is the longer side in this case.
So, the length of the shorter side is x
Shorter side = 9 units