Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If $x$ is the length of a median of an equilateral triangle, then its area is
(a)$x^{2}$
(b)$\frac{1}{2} x^{2}$
(c)$\frac{\sqrt{3}}{2} x^{2}$
(d)$\frac{\sqrt{3}}{3} x^{2}$
Answer
Answer (as printed): D
Explanation
Let the side of the triangle be $a$. Then, $$\begin{aligned} & a^{2}=\left(\frac{a}{2}\right)^{2}+x^{2} \Leftrightarrow \frac{3 a^{2}}{4}=x^{2} \Leftrightarrow a^{2}=\frac{4 x^{2}}{3} . \\ & \therefore \quad \text { Area }=\frac{\sqrt{3}}{4} a^{2}=\frac{\sqrt{3}}{4} \times \frac{4}{3} x^{2}=\frac{x^{2}}{\sqrt{3}}=\frac{x^{2} \sqrt{3}}{3} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.