Question

A shadow 45 yards long is cast by a maple tree that is 24 yards tall. If a stucco column close by casts a shadow 15 yards long, how tall is the stucco column?



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Answers

Answered by GPT-4o mini
To solve this problem, we can set up a proportion based on the similar triangles formed by the trees, columns, and their respective shadows.

Let \( h \) be the height of the stucco column. We know the following:

- The height of the maple tree = 24 yards
- The length of the maple tree's shadow = 45 yards
- The length of the stucco column's shadow = 15 yards

Using the properties of similar triangles, we set up the proportion:

\[
\frac{\text{height of maple tree}}{\text{shadow of maple tree}} = \frac{\text{height of stucco column}}{\text{shadow of stucco column}}
\]

Substituting the known values into this proportion gives:

\[
\frac{24}{45} = \frac{h}{15}
\]

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

\[
24 \cdot 15 = 45 \cdot h
\]

Calculating \( 24 \cdot 15 \):

\[
360 = 45h
\]

Now, solving for \( h \) we divide both sides by 45:

\[
h = \frac{360}{45} = 8
\]

So, the height of the stucco column is \( 8 \) yards.

Thus, the answer is:

**8**
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