If both perpendiculars on the diagonal of a quadrilateral are doubled while the diagonal stays the same, the…

If both perpendiculars on the diagonal of a quadrilateral are doubled while the diagonal stays the same, the new area is:
  1. Same as before
  2. Doubled
  3. Tripled
  4. Four times

Solution

Area $= \dfrac{1}{2} d (h_{1}+h_{2})$. Doubling both heights gives $\dfrac{1}{2} d (2h_{1}+2h_{2}) = 2 \cdot \dfrac{1}{2} d (h_{1}+h_{2})$, twice the original area.

Asked in: IMO

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