A pole $6$ m high casts a shadow $4$ m long. At the same time, a tree casts a shadow $14$ m long. The height…

A pole $6$ m high casts a shadow $4$ m long. At the same time, a tree casts a shadow $14$ m long. The height of the tree is:
  1. $18$ m
  2. $20$ m
  3. $21$ m
  4. $24$ m

Solution

Heights and shadows are directly proportional: $\dfrac{h}{14} = \dfrac{6}{4}$, so $h = \dfrac{6 \times 14}{4} = 21$ m.

Asked in: IMO

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