Question : ABC is an equilateral triangle. If the area of the triangle is $36 \sqrt{3}$, then what is the radius of the circle circumscribing the $\triangle ABC$?
Option 1: $2 \sqrt{3}$
Option 2: $3 \sqrt{3}$
Option 3: $4 \sqrt{3}$
Option 4: $6 \sqrt{3}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $4 \sqrt{3}$
Solution : Given: ABC is an equilateral triangle. The area of the triangle is $36 \sqrt{3}$. The area of the equilateral triangle $=\frac{\sqrt3}{4}\times (s)^2$, where $s$ is the sides of the triangle. The radius of the circle circumscribing the equilateral triangle $=\frac{s}{\sqrt3}$. ⇒ $\frac{\sqrt3}{4}\times (s)^2= 36 \sqrt{3}$ ⇒ $(s)^2=4\times 36$ ⇒ $s = 2\times 6=12$ units The radius of the circle circumscribing the $\triangle ABC$ $=\frac{12}{\sqrt3}=4\sqrt3$. Hence, the correct answer is $4 \sqrt{3}$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm. What is the ratio of the radius of the circle inscribed in it to the radius of the circle circumscribing $\triangle ABC$?
Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?
Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?
Question : The side of an equilateral triangle is 36 cm. What is the radius of the circle circumscribing this equilateral triangle?
Question : The length of the altitude of an equilateral triangle is $6 \sqrt{3}\;m$. The perimeter of the equilateral triangle (in m) is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile