A pole of $8$ m height casts a $10$ m long shadow. Find the height of the tree that casts a $40$ m long shadow under similar conditions.

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Solution

Length of a shadow directly varies to the height of the pole
So $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$ Here $x_{1} = 8 m$ $y_{1} = 10 m$ $x_{2} = ?$ and $y_{2} = 40 m$
Substitute $\frac{8}{10} = \frac{x_{2}}{40}$ $\Rightarrow$ $x_{2} = \frac{8 \times 40}{10} = 32 m$
So height of the tree is $32 m$

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