To solve this problem using the concept of similar triangles, we can set up a proportion based on Hashim's height and shadow length compared to the height and shadow length of the tree.
First, we need to convert Hashim's height to inches:
- Hashim's height is 5 feet 2 inches, which is \(5 \times 12 + 2 = 60 + 2 = 62\) inches.
Now let's denote:
- Hashim's height: 62 inches
- Hashim's shadow: 124 inches
- Tree's height: 20 feet (which is \(20 \times 12 = 240\) inches)
- Tree's shadow: \(x\) inches (the unknown we want to find)
Setting up the proportion using similar triangles, we get:
\[ \frac{\text{Hashim's height}}{\text{Hashim's shadow}} = \frac{\text{Tree's height}}{\text{Tree's shadow}} \]
Substituting the known values:
\[ \frac{62}{124} = \frac{240}{x} \]
Cross-multiplying gives us:
\[ 62x = 240 \times 124 \]
Calculating \(240 \times 124\):
\[ 240 \times 124 = 29760 \]
So the equation becomes:
\[ 62x = 29760 \]
Now, solve for \(x\):
\[ x = \frac{29760}{62} \]
Calculating \(x\):
\[ x \approx 480 \text{ inches} \]
Now, to convert inches back to feet, we divide by 12:
\[ 480 \text{ inches} = \frac{480}{12} = 40 \text{ feet} \]
Thus, the length of the shadow of the 20-foot tree is 480 inches or 40 feet.
The correct answer is: 480 inches or 40 feet.
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