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In a right angle triangle,s a and s b denote the medians that belong to the legs of triangle,the median belonging to hypotenuse is s c . Find the Maximum value of the expression s a +s c ÷ s c .

In a right angle triangle,sa and sb denote the medians that belong to the legs of triangle,the median belonging to hypotenuse is sc . Find the Maximum value of the expression sa+sc÷ sc .  

Grade:12th pass

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
The lengths of medians of triangle sa,sb,sc are given by
sa=\sqrt{\frac{2b^{2}+2c^{2}-a^{2}}{4}}
sb=\sqrt{\frac{2c^{2}+2a^{2}-b^{2}}{4}}
sc=\sqrt{\frac{2a^{2}+2b^{2}-c^{2}}{4}}
But in a right angled triangle\angle B=90(since given c as hypotenuese)
also c2=a2+b2
so sc=c/2
so (sa+sc)/sc=1+(sa/sc)=1+(\sqrt{4b^{2}+a^{2}}/c)
Thanks and Regards
Shaik Aasif
askIITians faculty

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