In Delta ABC,overline{AD} is a median. If AB | vedclass

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(A) According to Apollonius's theorem for $\Delta ABC$ with median $\overline{AD}$:$AB^2 + AC^2 = 2(AD^2 + BD^2)$Given that $\overline{AD}$ is a media

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(A) According to Apollonius's theorem for $\Delta ABC$ with median $\overline{AD}$:$AB^2 + AC^2 = 2(AD^2 + BD^2)$Given that $\overline{AD}$ is a median to side $\overline{BC}$,$D$ is the midpoint of $\overline{BC}$.Therefore,$BD = DC = \frac{BC}{2} = \frac{18}{2} = 9$.Substituting the given values into the theorem:$8^2 + AC^2 = 2(7^2 + 9^2)$$64 + AC^2 = 2(49 + 81)$$64 + AC^2 = 2(130)$$64 + AC^2 = 260$$AC^2 = 260 - 64$$AC^2 = 196$$AC = \sqrt{196} = 14$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$BC = 18$,and $AD = 7$,then $AC = \ldots$

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