Question
A tree casts a shadow of 28 feet. At the same time, a biologist who is 7 feet tall casts a shadow of 2 feet.
How tall is the tree?
98 feet
14 feet
78 feet
8 feet
How tall is the tree?
98 feet
14 feet
78 feet
8 feet
Answers
GPT-4o mini
To find the height of the tree, we can use the concept of similar triangles. The ratios of the heights of the objects to the lengths of their shadows should be the same.
Let \( h \) be the height of the tree. We can set up the following proportion based on the information provided:
\[
\frac{h}{28} = \frac{7}{2}
\]
Now, we can cross-multiply to solve for \( h \):
\[
h \cdot 2 = 7 \cdot 28
\]
Calculating the right side:
\[
h \cdot 2 = 196
\]
Now, divide both sides by 2 to find \( h \):
\[
h = \frac{196}{2} = 98 \text{ feet}
\]
Therefore, the height of the tree is **98 feet**.
Let \( h \) be the height of the tree. We can set up the following proportion based on the information provided:
\[
\frac{h}{28} = \frac{7}{2}
\]
Now, we can cross-multiply to solve for \( h \):
\[
h \cdot 2 = 7 \cdot 28
\]
Calculating the right side:
\[
h \cdot 2 = 196
\]
Now, divide both sides by 2 to find \( h \):
\[
h = \frac{196}{2} = 98 \text{ feet}
\]
Therefore, the height of the tree is **98 feet**.