Question

If G is the centroid of a triangle ABC and the median AD is 21 cm ,then find the value of DG

Answer 1

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Answer 2

The length of DG = 7 cm

Correct question : If G is the centroid of a triangle ABC and the median AD is 21 cm ,then find the length of DG

Given :

G is the centroid of a triangle ABC and the median AD is 21 cm

To find :

The length of DG

Solution :

Step 1 of 2 :

Form the equation to find length of DG

G is the centroid of a triangle ABC

The median AD is 21 cm

Since G divides AD in the ratio 2 : 1

Let AG = 2x cm and DG = x cm

By the given condition

2x + x = 21

Step 2 of 2 :

Calculate length of DG

2x + x = 21

⇒ 3x = 21

⇒ x = 21/3

⇒ x = 7

AG = 2x cm = 2 × 7 = 14 cm

DG = x cm = 7 cm

Hence length of DG = 7 cm

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