Chimney and tree

Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.

Correct result:

h₁ =  15.6 m

Solution:

$$\begin{gathered} h_1:h_2=t_1:t_2 \\ {t}_1=6.5\text{ m } \\ {h}_2=6\text{ m } \\ {t}_2=25\text{ dm}\to \text{ m}=25\mathrm{/}10\text{ m}=2.5\text{ m } \\ {h}_1=h_2\cdot {\displaystyle \frac{t_1}{t_2}}=6\cdot {\displaystyle \frac{6.5}{2.5}}={\displaystyle \frac{78}{5}}={\displaystyle \frac{78}{5}}\text{ m}=15.6\text{ m} \end{gathered}$$

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