the perimeter of a rectangle is 66cm and it's width is half its length. what are the length and width of the rectangle

Question

Please help me find the answer

Answer 1

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 

Comments

You had 54 instead of 66 as the perimeter. Take a look at the solution and try to understand how it works. Copying an answer from the Internet can be helpful, but you need to check that all the figures are correct! But it was clever of you to discover an answer. 

Answer 2

Well the equation for perimeter is 2l + 2w = p
and l = 2w (because it's half the length)
so just substitute:
2(2w) + 2w = 66
4w + 2w = 66
6w = 66
w = 11
and since the width is half, l = 22

Thus, length is 22 and width is 11

Geometry Help