What is the <strong>MAXIMUM</strong> area of the triangle?
Consider the following for the two (02) items that follow : Let ABC be a triangle right-angled at B and AB+AC=3 units.
- A. \sqrt{3}/2 square unit ✓
- B. \sqrt{3} square units
- C. \sqrt{6}/2 square units
- D. \sqrt{6} square units
Correct Answer: A. \sqrt{3}/2 square unit
Explanation
For maximum area, c = 1 and a^2 = 9 - 6(1) = 3 \implies a = \sqrt{3}. The maximum area \Delta = \frac{1}{2}ac = \frac{1}{2}(\sqrt{3})(1) = \frac{\sqrt{3}}{2} square units.
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