In `DeltaABC`, if `m_(a),m_(b),m_(c)` denote the lengths of the medians drawn to the sides a, b, c respectively and `Delta` is the area of the `DeltaABC` with `a=10, c=6" and "m_(b)=7`then

Options

A. `b=sqrt(76)`
B. `Delta=15sqrt(3)`
C. `m_(a)=sqrt(76)`
D. `m_(c)=sqrt(31)`

Answer

A

Explanation

`m_(b)=(1)/(2)sqrt(2a^(2)+2c^(2)-b^(2))`
`b^(2)=76impliesb=sqrt(76)=2sqrt(19),s=(a+b+c)/(2)=8+sqrt(19)`
`Delta=sqrt(s(s-a)(s-b)(s-c))=15sqrt(3)`
`m_(a)=(1)/(2)sqrt(2b^(2)+2c^(2)-a^(2))=sqrt(31)`
`m_(c)=(1)/(2)sqrt(2a^(2)+2b^(2)-c^(2))=sqrt(79).`Ans.