UPSC CDS I 2025 Mathematics Paper

The sum of the squares of medians of a triangle is given by:
Sum of squares of medians =‌

3

4

(a2+b2+c2)
Where, a,b, and c are the sides of the triangle.
Calculation:
Let a=k,b=1.5k=3k∕2,c=2.25k=9k∕4.
a2+b2+c2=k2+‌

9

4

k2+‌

81

16

k2
a2+b2+c2=‌

16

16

k2+‌

36

16

k2+‌

81

16

k2=‌

133

16

k2
Sum of squares of medians =‌

3

4

×‌

133

16

k2
Sum of squares of medians =‌

3×133

4×16

k2=‌

399

64

k2