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

`24`
`\text{cm}`

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}`
`=(3)/(2)\text{AG}`

`=(3)/(2)*16`

`=24\text{cm}`

length of
`\text{BE}`
`=(3)/(2)\text{BG}`

`=(3)/(2)*17`

`=(51)/(2)\text{cm}`

length of
`\text{CF}`
`=(3)/(2)\text{CG}`

`=(3)/(2)*18`

`=27\text{cm}`

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