Awoman w = 5 ft tall is standing near a street lamp that is s = 14 ft tall, as shown in the figure. find a function that models the length l of her shadow in terms of her distance d from the base of the lamp.

Here we use similar triangles. The height of the lamp is to the end of the shadow, the length of the shadow will be (d+l) as the woman's height is 5 ft, the length of the woman's shadow will be l.
Thus we shall have the following similarity
(height of the SL)/(length of the shadow of SL)=(height of the woman)/(length of her shadow)
hence
14/(d+l)=5/l

cross multiplying we get
14l=5(d+l)
14l=5d+5l
9l=5d
l=5/9d
the function can be written as
l(d)=5/9d