A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 24 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.

Question

14.6 feet
11.6 feet
9.6 feet
4.8 feet

Answer 1

To find the length of the tree's shadow, we can set up a proportion using the heights and shadows of the fence post and tree.

Height of fence post = 5 feet
Shadow of fence post = 2 feet
Height of tree = 24 feet
Shadow of tree = x (unknown)

Using the proportions:
5/2 = 24/x

Cross multiplying, we get:
5x = 48
x = 48/5
x = 9.6 feet

Therefore, the length of the tree's shadow is 9.6 feet.

Correct answer: 9.6 feet