Question
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Question
A tree casts a shadow 180 inches long. At the same time, a nearby fire hydrant measuring 24 inches tall casts a shadow 60 inches long. What is the height of the tree?(1 point)
Responses
72 inches
72 inches
450 inches
450 inches
90 inches
90 inches
8 inches
Answers
GPT-4o mini
To find the height of the tree using proportions, we can set up a ratio based on the information given:
Let \( h \) be the height of the tree.
The ratio of the height of the fire hydrant to its shadow is equal to the ratio of the height of the tree to its shadow:
\[
\frac{\text{height of hydrant}}{\text{shadow of hydrant}} = \frac{\text{height of tree}}{\text{shadow of tree}}
\]
Substituting the known values:
\[
\frac{24 \text{ inches}}{60 \text{ inches}} = \frac{h}{180 \text{ inches}}
\]
Now, cross-multiply to solve for \( h \):
\[
24 \cdot 180 = 60 \cdot h
\]
This simplifies to:
\[
4320 = 60h
\]
Now, divide both sides by 60:
\[
h = \frac{4320}{60} = 72
\]
Thus, the height of the tree is **72 inches**.
Let \( h \) be the height of the tree.
The ratio of the height of the fire hydrant to its shadow is equal to the ratio of the height of the tree to its shadow:
\[
\frac{\text{height of hydrant}}{\text{shadow of hydrant}} = \frac{\text{height of tree}}{\text{shadow of tree}}
\]
Substituting the known values:
\[
\frac{24 \text{ inches}}{60 \text{ inches}} = \frac{h}{180 \text{ inches}}
\]
Now, cross-multiply to solve for \( h \):
\[
24 \cdot 180 = 60 \cdot h
\]
This simplifies to:
\[
4320 = 60h
\]
Now, divide both sides by 60:
\[
h = \frac{4320}{60} = 72
\]
Thus, the height of the tree is **72 inches**.