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?
Question 19 options:
6
10
8
12
Question 19 options:
6
10
8
12
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**
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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