Question : In an equilateral triangle ABC, D is the midpoint of side BC. If the length of BC is 8 cm, then the height of the triangle is:
Option 1: $5.5 \mathrm{~cm}$
Option 2: $4.5 \mathrm{~cm}$
Option 3: $6 \sqrt{3} \mathrm{~cm}$
Option 4: $4 \sqrt{3} \mathrm{~cm}$
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Correct Answer: $4 \sqrt{3} \mathrm{~cm}$
Solution :
Given: ABC is an equilateral triangle.
D is the midpoint on side BC.
AB = BC = AC = 8 cm
We know that area of the equilateral triangle is $\frac{\sqrt3}{4}\times(\text{side})^2$
In $\triangle ABC$,
$\frac{\sqrt 3}{4}\times 8^2=\frac{1}{2}\times8\times AD$
$\therefore AD=4\sqrt3\ \text{cm}$
Hence, the correct answer is $4\sqrt3\ \text{cm}$.
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