An Alien is 5 feet tall. His shadow is 8 feet long. At the same time of the day, a tree's shadow is 32 feet long. What is the height of the tree?
20 feet
24 feet
29 feet
51 feet
O
We can set up a proportion to solve this problem. Let x be the height of the tree.
Since the alien's height is 5 feet and its shadow is 8 feet long, we have:
Alien's height/alien's shadow = tree's height/tree's shadow
5/8 = x/32
Cross-multiplying, we have:
8x = 5 * 32
8x = 160
Dividing both sides by 8, we get:
x = 20
Therefore, the height of the tree is 20 feet.
To find the height of the tree, we can use ratios to compare the lengths of the shadows with the heights of the objects.
The ratio of an object's height to the length of its shadow is the same as the ratio of the height of the alien to the length of its shadow.
So, the ratio of the alien's height to its shadow is 5 feet / 8 feet.
We can set up a proportion to find the height of the tree:
5 feet / 8 feet = h feet / 32 feet
To solve for h, we can cross multiply:
8 feet * h feet = 5 feet * 32 feet
8h = 160
Divide both sides by 8:
h = 160 / 8
h = 20
Therefore, the height of the tree is 20 feet.
So, the correct answer is "20 feet".
To find the height of the tree, we can use proportions. The height of the alien and its shadow length forms one ratio, and the height of the tree and its shadow length forms another ratio.
Let's call the height of the tree "x". We can set up the proportion:
(Height of Alien) / (Shadow of Alien) = (Height of Tree) / (Shadow of Tree)
Plugging in the known values:
5 feet / 8 feet = x / 32 feet
To solve for x, we can cross-multiply and solve for x:
5 feet * 32 feet = 8 feet * x
160 feet = 8 feet * x
Divide both sides by 8 feet:
160 feet / 8 feet = x
x = 20 feet
Thus, the height of the tree is 20 feet. So the correct answer is option A: 20 feet.