Question

If measured at the same moment, the length of a person's shadow varies directly with the height of the person. If a 3 foot child casts a 5 foot shadow, what is the length of the shadow of a 6 foot adult?​

Answer 1

10 ft

Explanation:

let l be length of shadow and h the height of a person

Given l varies directly with h then the equation relating them is

l = kh ← k is the constant of variation

To find k use the condition h = 3, l = 5 , then

5 = 3k ( divide both sides by 3 )

`(5)/(3)` = k

l =
`(5)/(3)` h ← equation of variation

When h = 6 , then

l =
`(5)/(3)` × 6 = 5 × 2 = 10 ft