Question

A tree cast a shadow of 12 meters when a 5 meter pole casts a shadow of 4 meters.How tall is the tree?

Answer 1

Using proportions derived from similar triangles, the height of the tree is calculated as 15 meters based on its shadow length and the known height and shadow length of a pole.

Step-by-step explanation:

The question involves using proportions to find the height of a tree based on the length of its shadow compared to the known height and shadow length of a pole. This is an application of similar triangles because the tree and the pole with their respective shadows form two similar triangles.

To solve this problem, we create a ratio comparing the heights to the shadows:

1. Height of pole / Shadow of pole = Height of tree / Shadow of tree
2. 5 meters / 4 meters = Height of tree / 12 meters
3. To find the height of the tree, we cross-multiply and divide:
4. (Height of tree * 4 meters) = (5 meters * 12 meters)
5. Height of tree = (5 meters * 12 meters) / 4 meters
6. Height of tree = 60 meters / 4 meters
7. Height of tree = 15 meters

Therefore, the height of the tree is 15 meters.