Q.455. - Intermediate Algebra

Question

Francesca is $5.75$ feet tall. Late one afternoon, her shadow was $8$ feet long. At the same time, the shadow of a nearby tree was $32$ ft long. Find the height of the tree.

Step-by-Step Solution

Answer

The height of the tree is $23$ feet.

Step 1. Given information.

The height of Francesca is $5.75$ feet tall and the height of her shadow was $8$ feet long.

At the same time the shadow of a nearby tree was $32$ feet long.

Step 2. To find the height of the tree.

Let $x$ represents the height of the tree.

The required proportion is:

$\frac{5.75}{8}=\frac{x}{32}$

Use cross-product property to solve the above proportion.

$$\begin{gathered} \frac{5.75}{8}=\frac{x}{32} \\ \left(5.75\right)\times 32=8x \\ x=\frac{\left(5.75\right)\times 32}{8} \\ x=\left(5.75\right)\times 4 \\ x=23 \end{gathered}$$

Step 3. Simplified answer.

Hence, the height of the tree is $23$ feet.