Question

A pine tree is 8 feet tall and its shadow is 15 feet long. A nearby redwood tree is 24 feet tall. How long is the redwood tree's shadow?

Question 20 options:

30


35


40


45

Answer 1

To find the length of the redwood tree's shadow, we can use the concept of similar triangles. The height of the pine tree and the length of its shadow can be set in proportion to the height of the redwood tree and the length of its shadow.

Let's denote:
- Height of the pine tree = 8 feet
- Length of the pine tree's shadow = 15 feet
- Height of the redwood tree = 24 feet
- Length of the redwood tree's shadow = \( x \)

We can set up the proportion as follows:

\[
\frac{\text{Height of pine tree}}{\text{Length of pine tree's shadow}} = \frac{\text{Height of redwood tree}}{\text{Length of redwood tree's shadow}}
\]

Substituting in the known values:

\[
\frac{8}{15} = \frac{24}{x}
\]

Now, we can cross-multiply to solve for \( x \):

\[
8x = 24 \times 15
\]

Calculating the right side:

\[
24 \times 15 = 360
\]

So our equation becomes:

\[
8x = 360
\]

Dividing both sides by 8 gives:

\[
x = \frac{360}{8} = 45
\]

Thus, the length of the redwood tree's shadow is **45 feet**.

The correct answer is **45**.