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.

Question

 
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.