Question

If the length of median AP of ∆ABC is 9 cm and G is the centroid then find l ( AG ) and l ( GP )





*with solution*​

Answer 1

Answer:

Correct option is

B

8cm

We know that G is centroid of ΔABC

AD=12cm

Centroid → intersection point of medians

Centroid divides median in ratio of 2:1

AD

AG

=

1

2

AG=2AD

AG+GD=12

3GD=12

GD=4cm

AG=8cm.

Answer 2

Given : Length of median AP of ∆ABC is 9 cm and G is the centroid of triangle.

To find : length of AG and GP.

Solution :

Median of a triangle from a vertex is the line that bisects the opposite side of the triangle to the vertex.

A triangle has three medians that bisect the three sides. The intersection of the medians is called centroid of the triangle.

Here, AP is the median and G the centroid of the triangle.

G divides the median in the ratio 1:2.

Since, length of AP is 9 cm, therefore AG:GP = 2:1

Therefore,

length of AG = 2 × 3 = 6 cm.

length of GP = 1 × 3 = 3 cm.