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:[tex]24[/tex] [tex]\text{cm}[/tex]Step-by-step explanation:Given: The distance from the centroid of a triangle to its vertices are [tex]16\text{cm}[/tex], [tex]17\text{cm}[/tex], and [tex]18\text{cm}[/tex].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 [tex]\text{AG}[/tex] [tex]=16\text{cm}[/tex]length of [tex]\text{BG}[/tex] [tex]=17\text{cm}[/tex]length of [tex]\text{CG}[/tex] [tex]=18\text{cm}[/tex]as centrod divides median in ratio of [tex]2:1[/tex]length of [tex]\text{AD}[/tex] [tex]=\frac{3}{2}\text{AG}[/tex] [tex]=\frac{3}{2}\times16[/tex] [tex]=24\text{cm}[/tex]length of [tex]\text{BE}[/tex] [tex]=\frac{3}{2}\text{BG}[/tex] [tex]=\frac{3}{2}\times17[/tex] [tex]=\frac{51}{2}\text{cm}[/tex]length of [tex]\text{CF}[/tex] [tex]=\frac{3}{2}\text{CG}[/tex] [tex]=\frac{3}{2}\times18[/tex] [tex]=27\text{cm}[/tex]Hence the shortest median is [tex]\text{AD}[/tex] of length [tex]24\text{cm}[/tex]