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Grade 12th passAlgebra

In a right angle triangle,s_a and s_bdenote 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 .}

saurabh

12 Years agoGrade 12th pass

1 Answer

SHAIK AASIF AHAMED

12 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

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