At a certain time of day, a vertical pole 8ft high casts a 5ft shadow. how long is the shadow of a 4ft child? choices provided in image.

We can look at 2 similar triangles.
1st triangle has legs: a vertical pole and its shadow, and
2nd triangle has legs legs : a child and his(her) shadow.

We can write a proportion:
height of a pole/height of a child= shadow of a pole/shadow of a child

8/4 = 5/shadow of a child
shadow of a child=(5*4)/8=5/2 ft
5/2 ft