Question

An object's height varies directly with the length of its shadow. A person who is 5 feet tall casts an 8-foot shadow. How long is the shadow of a 20-foot tree?

Answer 1

The tree is 12.5 ft. tall.

Answer 2

32 feet.

Explanation:

We have been given that the height of an object varies directly with the length of its shadow.

Let y represent length of shadow and x represent height. So our required equation would be
`y=kx`, where, k is constant of proportionality.

Let us solve for k by substituting
`x=5` and
`y=8`.

`8=k*5`

`(8)/(5)=(k*5)/(5)`

`(8)/(5)=k`

`y=(8)/(5)x`

To find the shadow of a 20-ft tree, we will substitute
`x=20`.

`y=(8)/(5)*20`

`y=8*4`

`y=32`

Therefore, the shadow of tree is 32 feet.