homework help please.?

Question

it is sort of a word problem.
Fred walks alon a level path directly away from a streetlight. If fred is 6ft tall and the street light is 15ft tall. how long is freds shadow when he is 5 ft away from the street light.

most detailed answer gets the points

thanks for your help

Answer 1

This makes similar triangles so the legs of the triangles will be proportianal: if x= shadow
6/15=x/(5+x)
6(5+x)=15x
30+6x=15x
30=9x
x=10/3 ft

Answer 2

Draw a diagram, with a line from the streetlight to Fred's head to the ground. We have two similar right triangles (they share a vertex and both have right angles at the same side of it, so corresponding angles are equal and they are similar); one has a height of 6 ft and the other 15 ft. If the length of Fred's shadow is x ft, then the base of the smaller triangle is x ft and the base of the larger triangle is (x+5) ft.

Because the triangles are similar, the ratio of the base to the height is the same for each. So we have
x / 6 = (x+5) / 15
and thus (multiplying both sides by 30)
5x = 2x + 10
<=> 3x = 10
<=> x = 10/3.
So Fred's shadow is 10/3 ft = 3ft 4in long.