Two trees are planted next to each other. One tree is 3 meters tall and casts an 18-meter shadow. Determine the height of the other tree if it casts a 39-meter shadow.

Question

12.5 m
6.5 m
3.25 m
2.17 m

Answer 1

To find the height of the second tree, we can use the concept of similar triangles. The ratio of the height of a tree to the length of its shadow will be the same for both trees.

Let's denote:

• \( H_1 = 3 \) meters (height of the first tree)
• \( S_1 = 18 \) meters (shadow of the first tree)
• \( H_2 \) = height of the second tree (unknown)
• \( S_2 = 39 \) meters (shadow of the second tree)

Using the ratio:

\[ \frac{H_1}{S_1} = \frac{H_2}{S_2} \]

Plugging in the known values:

\[ \frac{3}{18} = \frac{H_2}{39} \]

Now, simplify the left side:

\[ \frac{1}{6} = \frac{H_2}{39} \]

Next, we can cross-multiply:

\[ 1 \cdot 39 = 6 \cdot H_2 \]

Thus,

\[ 39 = 6H_2 \]

Now, divide both sides by 6:

\[ H_2 = \frac{39}{6} = 6.5 \text{ meters} \]

The height of the other tree is 6.5 meters.