Question
A 24 ft tall tree casts a shadow 10 feet long. Brad is 6 feet tall. How long is Brad's Shadow?
Answers
GPT-4o mini
To find the length of Brad's shadow, we can set up a proportion based on the height of the tree and the length of its shadow compared to Brad's height and shadow.
Let \( L \) be the length of Brad's shadow. The proportion can be set up as follows:
\[
\frac{\text{Height of the tree}}{\text{Length of the tree's shadow}} = \frac{\text{Height of Brad}}{\text{Length of Brad's shadow}}
\]
Substituting the known values:
\[
\frac{24 \text{ ft}}{10 \text{ ft}} = \frac{6 \text{ ft}}{L}
\]
Cross-multiplying to solve for \( L \):
\[
24 \cdot L = 10 \cdot 6
\]
\[
24L = 60
\]
Now, divide both sides by 24:
\[
L = \frac{60}{24} = 2.5 \text{ ft}
\]
Thus, Brad's shadow is \( 2.5 \) feet long.
Let \( L \) be the length of Brad's shadow. The proportion can be set up as follows:
\[
\frac{\text{Height of the tree}}{\text{Length of the tree's shadow}} = \frac{\text{Height of Brad}}{\text{Length of Brad's shadow}}
\]
Substituting the known values:
\[
\frac{24 \text{ ft}}{10 \text{ ft}} = \frac{6 \text{ ft}}{L}
\]
Cross-multiplying to solve for \( L \):
\[
24 \cdot L = 10 \cdot 6
\]
\[
24L = 60
\]
Now, divide both sides by 24:
\[
L = \frac{60}{24} = 2.5 \text{ ft}
\]
Thus, Brad's shadow is \( 2.5 \) feet long.