Question : The length of the median of an equilateral triangle is $12\sqrt3 \text{ cm}$. Then, the area of the triangle is:
Option 1: $144\text{ cm}^2$
Option 2: $288\sqrt3\text{ cm}^2$
Option 3: $144\sqrt3\text{ cm}^2$
Option 4: $288\text{ cm}^2$
Correct Answer: $144\sqrt3\text{ cm}^2$
Solution :
Given: The length of the median of an equilateral triangle is $12\sqrt3\text{ cm}$.
The height of an equilateral triangle of the side $x$ is $\frac{\sqrt3}{2} x$ and its area is given as $\frac{\sqrt3}{4} x^2$.
According to the question,
$\frac{\sqrt3}{2} x =12\sqrt3 $
⇒ $x=24\text{ cm}$
Then, the area of the triangle is given as,
$\frac{\sqrt3}{4}\times x^2$
$=\frac{\sqrt3}{4}\times (24)^2$
$=144\sqrt3\text{ cm}^2$
Hence, the correct answer is $144\sqrt3\text{ cm}^2$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
