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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Apollonius's Theorem,for any triangle $ABC$ with median $AD$ to side $BC$:$AB^2 + AC^2 = 2(AD^2 + BD^2)$Given $AB = 10$,$AC = 24$,and

Vedclass · Accepted Answer

$26$

Vedclass · Answer

(B) According to Apollonius's Theorem,for any triangle $ABC$ with median $AD$ to side $BC$:$AB^2 + AC^2 = 2(AD^2 + BD^2)$Given $AB = 10$,$AC = 24$,and $AD = 13$.Substituting the values:$10^2 + 24^2 = 2(13^2 + BD^2)$$100 + 576 = 2(169 + BD^2)$$676 = 2(169 + BD^2)$$338 = 169 + BD^2$$BD^2 = 338 - 169 = 169$$BD = \sqrt{169} = 13$Since $AD$ is a median,$D$ is the midpoint of $BC$,so $BC = 2 	imes BD$.$BC = 2 	imes 13 = 26$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 10$,$AC = 24$,and $AD = 13$,find $BC$.

Similar Questions

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{AB} \cong \overline{BC}$. Find the ratio $AB : AC$.

Diagonals of convex quadrilateral $ABCD$ intersect at $O$. If $OA \times OD = OB \times OC$,prove that $AB \parallel CD$.

Using Theorem $6.1,$ prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$. If $XY = a^{2} - b^{2}$ and $YZ = 2ab$,find $XZ$ (where $a > b > 0$).

$ABC$ is an equilateral triangle of side $2a$. Find each of its altitudes.

Vedclass Test Series

Exam Paper Generator

Online Exam Module