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: $4 \sqrt{3} \mathrm{~cm}$

Question

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: $4 \sqrt{3} \mathrm{~cm}$

Team Careers360 · Accepted Answer

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 $\frac{\sqrt3}{4} imes( ext{side})^2$
In $ riangle ABC$,
$\frac{\sqrt 3}{4} imes 8^2=\frac{1}{2} imes8 imes AD$
$ herefore AD=4\sqrt3\ ext{cm}$
Hence, the correct answer is $4\sqrt3\ ext{cm}$.

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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 cmOption 2: 4.5 cmOption 3: 63 cmOption 4: 43 cm

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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: $5.5 cm$
Option 2: $4.5 cm$
Option 3: $6 \sqrt{3} cm$
Option 4: $4 \sqrt{3} cm$