Question

A park has a 3 meter tall tether ball pole and a 6.8 m tall flagpole. The lengths of their shadows are proportional to their heights.

Which of the following could be the lengths of the shadows?

Choose 2 answers:

The answer is B and d

Answer 1

B & D

Explanation:

I got it right on Khan Academy.

Answer 2

The relationship between the height and shadow length is a direct proportionality type of relationship. That is, the higher the height, the longer the shadow and vice versa. The ratio of height to shadow length is a constant.
Therefore, if x and y are are the length of shadow of tether ball pole and flagpole receptively,


`(6.8)/(y)` =
`(3)/(x)` => y=
`(6.8)/(3)x`

When x= 1.35 m
y=(6.8/3)*1.35 =3.06 m
When x=1.8 m
y= (6.8/3)*1.8 = 4.08 m
When x= 3.75 m
y=(6.8/3)*3.75 = 8.5 m
When x= 0.6
y= (6.8/3)*0.6 = 1.36 m
When x=2
y= (6.8/3)*2 = 4.533 m

Therefore, it is true that B and D are the true answers.