Question

A telephone pole 10 meters tall casts a shadow 8 meters long at the same time that a tree nearby casts a shadow 14 meters long. How tall is the tree?
19
20
16
17.5

Answer 1

To solve for the height of the tree using the proportional relationship between the height of the pole and its shadow, we can set up a proportion based on the information given.

Let \( h \) be the height of the tree. We know:

- Height of the pole = 10 meters
- Length of the pole's shadow = 8 meters
- Length of the tree's shadow = 14 meters

The relation can be expressed as:

\[
\frac{\text{Height of the pole}}{\text{Length of the pole's shadow}} = \frac{\text{Height of the tree}}{\text{Length of the tree's shadow}}
\]

Substituting the known values:

\[
\frac{10}{8} = \frac{h}{14}
\]

Now, cross-multiply to solve for \( h \):

\[
10 \times 14 = 8 \times h
\]

\[
140 = 8h
\]

Now, divide both sides by 8:

\[
h = \frac{140}{8} = 17.5
\]

Thus, the height of the tree is **17.5 meters**.