Are You Joking?
There Is A Right Triangle Whose Hypoteneuse(Longest Side Or The Side Opposite To The Right Angle)
Is Of Length 20 units . Find The Sum Of Squares Of Lengths Of Medians Of The Triangle.
Details And Assumptions
-
Median Is A Line Segment From Any Vertex Of The Triangle Which Has Its Other End Point As
The Midpoint Of Opposite Side .
-
Sum Of Square Of Lengths Means If You Get 3,4,5 as the answer
then enter the answer as 3^2+4^2+5^2 = 50
3.If You Think Data Is Insufficient Then Enter The Answer As Zero (0).
The answer is 600.
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Today In The Morning I Was Looking At The Derivation Of The Formula Of Length Of Medians Of A
Triangle. Then I Noticed That If We Wish To Find The Sum Of Squares Of Medians We Can Get A Nice
Result = 3/4(a^2+b^2+c^2) . Then On Further Observation I Observed That For A Right Triangle The
Result Can Be Simplified To 3/2(c^2) by using the pythagorean identity . Where c is length of longest side)
Well I Dont Know That This Observation Was Made Earlier Or Not By Anyone(But I Think It Would Have
Been Made Because It Is Not A Great Thing To Observe) :P
Well The Result Can Be Derived Easily Using Apollonius Theorem .
In A Triangle ABC Where AD Is the median