Question

Allison is 5 feet tall. One afternoon her shadow measured 2.5 feet. At the same time, the shadow of her favorite tree was 14.5 feet.
 
What is the height of the tree?

Answer 1

To find the height of the tree using similar triangles, we can set up a proportion based on the height and the shadow lengths of Allison and the tree.

Let:
- \( h \) = height of the tree
- Height of Allison = 5 feet
- Shadow of Allison = 2.5 feet
- Shadow of the tree = 14.5 feet

The proportion based on the similar triangles is:

\[
\frac{\text{Height of Allison}}{\text{Shadow of Allison}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]

Plugging in the values, we get:

\[
\frac{5}{2.5} = \frac{h}{14.5}
\]

Now, we can simplify the left side:

\[
\frac{5}{2.5} = 2
\]

So the equation becomes:

\[
2 = \frac{h}{14.5}
\]

To find \( h \), we multiply both sides by 14.5:

\[
h = 2 \times 14.5
\]

Calculating this gives:

\[
h = 29
\]

Thus, the height of the tree is **29 feet**.