Question : $G$ is the centroid of the equilateral triangle $ABC$. If $AB$ is $9\text{ cm}$, then $AG$ is equal to:
Option 1: $3 \sqrt 3\text{ cm}$
Option 2: $3\text{ cm}$
Option 3: $\frac{3 \sqrt 3}{2}\text{ cm}$
Option 4: $6 \text{ cm}$
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: $3 \sqrt 3\text{ cm}$
Solution : The side of an equilateral triangle ($a$) $=9\text{ cm}$ Median $AD$ of equilateral triangle $=\frac{\sqrt{3}}{2}a$ ⇒ ${AD} = \frac{\sqrt{3}}{2}\times 9$ Also, a centroid divides the median in the ratio of $2:1$. So, $ AG : GD = 2 : 1$ ⇒ $\frac{AG}{AD}=\frac{2}{3}$ ⇒ $AG = \frac{2}{3} \times AD$ ⇒ $AG= \frac{2}{3} \times \frac{\sqrt{3}}{2}\times 9 = 3\sqrt{3}$ Hence, the correct answer is $3\sqrt{3}\text{ cm}$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : G is the centroid of the equilateral triangle ABC. If AB = 10 cm, then the length of AG (in cm) is:
Question : $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median. Find the length of GD if G is the centroid of $\triangle ABC$.
Question : The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:
Question : Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is:
Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile