Question

The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median

Answer 1

Answer:

$24$ $\text{cm}$

Step-by-step explanation:

Given: The distance from the centroid of a triangle to its vertices are $16\text{cm}$, $17\text{cm}$, and $18\text{cm}$.

To Find: Length of shortest median.

Solution:

Consider the figure attached

A centroid is an intersection point of medians of a triangle.

Also,

A centroid divides a median in a ratio of 2:1.

Let G be the centroid, and vertices are A,B and C.

length of $\text{AG}$ $=16\text{cm}$

length of $\text{BG}$ $=17\text{cm}$

length of $\text{CG}$ $=18\text{cm}$

as centrod divides median in ratio of $2:1$

length of $\text{AD}$ $=\frac{3}{2}\text{AG}$

                                              $=\frac{3}{2}\times16$

                                              $=24\text{cm}$

length of $\text{BE}$ $=\frac{3}{2}\text{BG}$

                                              $=\frac{3}{2}\times17$

                                              $=\frac{51}{2}\text{cm}$

length of $\text{CF}$ $=\frac{3}{2}\text{CG}$

                                              $=\frac{3}{2}\times18$

                                              $=27\text{cm}$

Hence the shortest median is $\text{AD}$ of length $24\text{cm}$