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Question 17

In $$\triangle ABC $$, $$AB=6\text{cm}$$, $$AC=8\text{cm}$$, median $$AD=5\text{cm}$$. Then, the area of $$ \triangle ABC $$ in $$\text{cm}^2$$ is


Correct Answer: 24

Solution

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Using the median length formula, $$AD^2=\frac{2AB^2+2AC^2-BC^2}{4}$$ gives $$BC^2=100$$. Since $$AB^2+AC^2=36+64=100=BC^2$$, the triangle is right angled at $$A$$, so its area is $$\frac{1}{2}\times6\times8=24$$.

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