let

w = the width of the rectangle

l = the length of the rectangle

the area of a rectangle is not more than 800

l*w <= 800

the width of the rectangle is twice the length

w = 2l

plug w into the inequality

l*2l <= 800

2l^2 <= 800 divide both sides by 2

l^2 <= 400

l <= 20

w = 2l <= 40

w <= 40

the dimensions of the rectangle are: the width is not more than 40 and the length is not more than 20.