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?

Question

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1 point
20 feet
24 feet
29 feet
51 feet

Answer 1

To find the height of the tree based on the given information about the alien and its shadow, we can use the concept of similar triangles.

Given:

• Height of the alien = 5 feet
• Length of the alien's shadow = 8 feet
• Length of the tree's shadow = 32 feet

Let \( h \) be the height of the tree. We can set up the proportion based on the similar triangles formed by the alien and its shadow, and the tree and its shadow:

\[ \frac{\text{Height of Alien}}{\text{Shadow of Alien}} = \frac{\text{Height of Tree}}{\text{Shadow of Tree}} \]

Substituting the values:

\[ \frac{5}{8} = \frac{h}{32} \]

Now, we can cross-multiply to solve for \( h \):

\[ 5 \cdot 32 = 8 \cdot h \] \[ 160 = 8h \]

Now, divide both sides by 8:

\[ h = \frac{160}{8} = 20 \]

So, the height of the tree is 20 feet.

Thus, the answer is 20 feet.