Question

Jack is 5 1/2 feet tall and casts a 9-ft shadow. At the same time, a basketball hoop casts a 24-foot Shadow. How tall is the basketball hoop?

Answer 1

The height of the basketball hoop is

`14 (2)/(3) ft`

Step-by-step explanation

Let the height of the basketball hoop be x feet.

The shadow of the basketball hoop is 9 ft long.

The height of Jack is 5.5 feet.

Jack's shadow is 9 ft long.

By similar triangles,

`(x)/(5.5) = (24)/(9)`

Multiply both sides by 5.5

This gives us,

`x = (24)/(9) * 5.5`

`x = (132)/(9)`

`x = 14 (2)/(3)`

The height of the basketball hoop is 14⅔ feet