First let's state the formula for perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
OK, for this rectangle let's set the length equal to x
length = x
Now we are told that the width is one half it length.
So if the length is x then
width = 1/2*(x) or x/2
OK, the problem also tells us that the perimeter is 66 cm
Now we have everything we need to use the perimeter formula and solve for x
Perimeter = 2(length) + 2(width)
66 = 2(x) + 2(x/2)
66 = 2x + x
66 = 3x
22 = x
Answer: the length is 22 cm
Now use this value for length to find the width
width = x/2
width = 22/2
width = 11
Answer: the width is 11 cm
Check both answers by using the perimeter formula.
Perimeter = 2(length)+2(width)
66 = 2(22) + 2(11)
66 = 44 + 22
66 = 66