the perimeter of a rectangle is 66 cm and its width is half its length. what are the length and the width of the rectangle?
P = 2(l + w)
w = l/2
Plug in 'l/2' for 'w' in the equation with '66':
66 = 2(l + l/2)
66 = 2l + 2l/2
66 = 2l + l
66 = 3l
22 = l
So the length is 22.
Now plug this in to find the width.
66 = 2(22 + w)
66 = 44 + 2w
22 = 2w
11 = w
So the width is 11, and the length is 22.
Let's set width = w
Then length = 2w
We can set up the equation:
\(2(w+ 2w) = 66\)
\(2(3w) = 66\)
\(6w = 66\)
\(w = \frac{66}{6} = \boxed{11}\)
Then we plug in:
\(l = 2w = 2(11) = \boxed{22}\)
Hope this helps :)