The width of a rectangle is half as long as as the length. The rectangle has an area of 50 square feet. What's the length and width?

W=1/2*L and Area=W*L=50

So,
W*L=50, or
(1/2*L)*L=50
1/2*L^2=50
L^2=100
L=10

and,
W=1/2*L, or
W=1/2*10
W=5