Question

if g is the centroid of triangle abc and bc=3,ca=4,ab=5 then bG=

Answer 1

Answer:

$\frac{ \sqrt{52} }{3}$

Answer 2

Concept introduction:

Centroid is considered as the midpoint in any triangular or quadrilateral structure. Centroid is considered as the main point of intersection of all the lines and angles present in a triangle.

Given:

We have been given g as the centroid of a triangle ABC. We have also given the sides of the triangle bc, ca, and ab as 3,4, and 5 respectively.

To find:

We need to find the centroid of the triangle and the measurement of the side bg.

Solution:

As per the question,

ab^2+bc^2=2(bd^2+ca)

or, 25+9=2(bd^2+4)

or, 34=2bd^2+8

or, 2bd^2=26

or, bd^2=13

Therefore, bd=root13

Therefote, bd=2/3*root 13

Therefore,

bg=2/3root 13

=2.403

Final answer:

BG=2.403

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