Question

On a sunny day a $2$ foot red kangaroo casts a shadow that is $7$ foot long shadow of a nearby eucalyptus tree is $14$ feet long. Find the height of the tree $?$

Answer 1

Find the height of the tree:

Let the height of kangaroo be ${\mathrm{h}}_1$ and the length of its shadow be ${\mathrm{x}}_1$.

${\mathrm{h}}_1=2\mathrm{ft},{\mathrm{x}}_1=7\mathrm{ft}$

Let the height of eucalyptus tree be ${\mathrm{h}}_2$ and the length of its shadow be ${\mathrm{x}}_2$.

${\mathrm{x}}_2=14\mathrm{ft}$

Since the length of shadow varies directly with the height at the same time of the day, the proportion is as follow:

$$\begin{gathered} \frac{{\mathrm{h}}_1}{{\mathrm{x}}_1}=\frac{{\mathrm{h}}_2}{{\mathrm{x}}_2} \\ \begin{array}{rcl}& \Rightarrow & \frac{2}{7}=\frac{{\mathrm{h}}_2}{14}\left[\because {\mathrm{h}}_1=2\mathrm{ft},{\mathrm{x}}_1=7\mathrm{ft}\mathrm{and}{\mathrm{x}}_2=14\right]\\ & \Rightarrow & 28=7{\mathrm{h}}_2\end{array} \end{gathered}$$

$\therefore {\mathrm{h}}_2=4$

Hence, the height of the eucalyptus tree is $\mathbf{4}\mathbf{}\mathbf{ft}.$