At 1 pm the shadow of a tree is 14 feet long. At the same time the shadow of a 18 foot telephone pole is 21 feet long. What is the height of the tree?
Responses
A9 feet
9 feet
B12 feet
12 feet
C18 feet
18 feet
D22 feet
22 feet
E24 feet
We can use proportions to solve this problem. Let's represent the height of the tree as x.
We know that the length of the shadow of the tree is 14 feet, and the length of the shadow of the telephone pole is 21 feet.
Using the proportional relationship between the heights and the shadows, we can set up the following equation:
(x / 14) = (18 / 21)
Cross multiplying, we get:
21x = 14 * 18
21x = 252
x = 252 / 21
x = 12
Therefore, the height of the tree is 12 feet.
The correct answer is:
B) 12 feet