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The medians AD and BE of the triangle wi...

The medians AD and BE of the triangle with vertices `A(0,b),B(0,0)` and `C(a,0)` are mutually perpendicular. Prove that `a^2=2b^2`.

Text Solution

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The correct Answer is:
NA

From the figure,
Slope of `BE,m_(BE)=(b)/(a)`
Slope of `AD,m_(AD)=-(2b)/(a)`
Given that AD and BE are perpendicular.
`therefore m_(BE)xxm_(AD)=-(2b^2)/(a^2)=-1`
`rArra^2=2b^2`
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