Hashim is 5 feet and 2 inches tall. His shadow is 124 inches. Using his height and shadow lengths, create a similar triangle to calculate the length of a shadow of a 20-foot tree.(1 point)

Question

Responses

120 inches or 10 feet
120 inches or 10 feet

240 inches or 20 feet
240 inches or 20 feet

480 inches or 40 feet
480 inches or 40 feet

360 inches or 30 feet

Answer 1

To solve the problem using similar triangles, we can set up a proportion based on Hashim's height and shadow length and the height and shadow length of the tree.

1. Convert Hashim's height into inches:

   • 5 feet = 5 × 12 inches = 60 inches
   • Add the 2 inches:
   • Total height = 60 inches + 2 inches = 62 inches

2. Now we have:

   • Hashim's height = 62 inches
   • Hashim's shadow = 124 inches

3. We need to find the shadow length of a 20-foot tree:

   • 20 feet = 20 × 12 inches = 240 inches

4. Set up the proportion: \[ \frac{\text{Height of Hashim}}{\text{Shadow of Hashim}} = \frac{\text{Height of Tree}}{\text{Shadow of Tree}} \]

   Plugging in the values: \[ \frac{62}{124} = \frac{240}{\text{Shadow of Tree}} \]

5. Cross-multiply to solve for Shadow of Tree: \[ 62 \times \text{Shadow of Tree} = 240 \times 124 \] \[ 62 \times \text{Shadow of Tree} = 29760 \]

6. Now divide by 62: \[ \text{Shadow of Tree} = \frac{29760}{62} = 480 \text{ inches} \]

Thus, the length of the shadow of a 20-foot tree is 480 inches or 40 feet.

The correct response is: 480 inches or 40 feet.