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.
14.6 feet
11.6 feet
9.6 feet
4.8 feet
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