Median Problem

Geometry Level 1

The lengths of the sides of a traingle are 5,6 and 10 cm respectively. Find the square of the length of the median of the greatest side.

2 solutions

Aryan Gaikwad
Mar 5, 2015

Let side $a = 10$ , $b = 6$ , $c = 5$ and median be ${ m }_{ a }$ .

Therefore, median =

${ m }_{ a }=\frac { \sqrt { 2{ b }^{ 2 }+2{ c }^{ 2 }-{ a }^{ 2 } } }{ 2 }$

On solving, we get that

${ m }_{ a }=\frac { \sqrt { 22 } }{ 2 }$

But the square of answer is asked. Therefore answer =

$({ \frac { \sqrt { 22 } }{ 2 } })^{ 2 }=\frac { 22 }{ 4 } =5.5$

Swapnil Das
Mar 2, 2015

Just a hint for now, use Appolonius Theorem.