Q:

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

Accepted Solution

A:
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 attachedA 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 $$24\text{cm}$$