If ABC is an equilateral triangle with side 12 cm and AD is the median. Find the length of GD if G is the centroid of ΔABC.

Question

Question

This question was previously asked in

SSC CHSL Memory Based Test (14th March 2023)

Answer 1

Given:

ABC is an equilateral triangle

AB = BC = CA = 12 cm

AD is the median of ΔABC

Concept used:

The point at which three medians of a triangle intersect is called the centroid of the triangle.

The centroid of a triangle divides medians in the ratio of 2 : 1

In an equilateral triangle median and perpendicular bisector of triangle coincide with each other

Calculation:

According to the question,

ΔABC is an equilateral triangle

So, AD is a perpendicular bisector of ΔABC

So, BD = CD = BC/2 and ∠ADB = 90°

Now, according to the Pythagoras theorem

AD² = AB²- (BC/2)²

⇒ AD2 = 12² - (12/2)²

⇒ AD2 = 144 - 36

⇒ AD = 6√3

Now, we have to find DG

DG = (1/3) × AD

⇒ DG = (1/3) × 6√3

⇒ DG = 2√3

∴ The length of DG is 2√3.

Download Solution PDF