Answer:
a) The perimeter of a rectangle is given by the formula:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width. We are given that the width of the rectangle is 2x and the length is three times the width. So we can set up an equation that represents the given information:
P = 2L + 2W
168 = 2(3W) + 2W
168 = 8W
b) To solve for W, we can divide both sides of the equation by 8:
168/8 = W
21 = W
Therefore, the width of the rectangle is 21cm.
c) To find the length of the rectangle, we can use the expression that represents the length in terms of the width:
L = 3W
L = 3(21)
L = 63
Therefore, the length of the rectangle is 63cm.
The width and length of the rectangle are 21cm and 63cm, respectively.