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

(D) According to Apollonius's Theorem,for any triangle $\Delta ABC$ with median $\overline{AD}$ to side $\overline{BC}$,the following relation holds:$

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) According to Apollonius's Theorem,for any triangle $\Delta ABC$ with median $\overline{AD}$ to side $\overline{BC}$,the following relation holds:$AB^2 + AC^2 = 2(AD^2 + BD^2)$Given that $AB^2 + AC^2 = 122$ and $AD = 6$,we substitute these values into the formula:$122 = 2(6^2 + BD^2)$$122 = 2(36 + BD^2)$Divide both sides by $2$:$61 = 36 + BD^2$$BD^2 = 61 - 36$$BD^2 = 25$$BD = \sqrt{25} = 5$Since $\overline{AD}$ is a median,$D$ is the midpoint of $\overline{BC}$,so $BC = 2 	imes BD$.$BC = 2 	imes 5 = 10$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB^2 + AC^2 = 122$ and $AD = 6$,find $BC$.

Similar Questions

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect at $O$. $\overrightarrow{AO}$ intersects $\overline{BC}$ at $P$. Prove that $\frac{AB}{AC} = \frac{BP}{PC}$.

Two adjacent sides of a rectangle measure $12$ and $35$. Then,the length of a diagonal of the rectangle is..........

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

In $\Delta XYZ$,the midpoints of the sides are $A, B$ and $C$. In $\Delta ABC$,the midpoints of the sides are $P, Q$ and $R$. If the area of $\Delta ABC$ is $24$,find the area of $\Delta XYZ$ and $\Delta PQR$.

$A$ $8 \, m$ long bamboo tree standing erect on the ground breaks at the height of $3 \, m$ from the ground. The broken part of the tree remains attached to the trunk. Find the distance in $m$ between the top of the tree on the ground and the base of the tree.

Vedclass Test Series

Exam Paper Generator

Online Exam Module