Question

plz solve this.... ....

Answer 1

$\underline{\underline{\bold{Question:}}}$

In the given figure ,

AB² + AC² = 122

BC = 10.

Find the length of the median on side BC.

$\tt{Solution:}$

We know that,

According to Apollonius Theorem ,

$\boxed{\bold{AB^2+AC^2=2[AQ^2+BQ^2]}}$

Where ,

• AQ = length of median.
• BQ = Half of BC.

So

A/Q,

$\implies\tt{AB^2+AC^2=2[AQ^2+BQ^2]}\\\\\\\implies\tt{122=2[AQ^2+5^2]}\\\\\\\implies\tt{122=2*AD^2+50}\\\\\\\implies\tt{2*AD^2=122-50}\\\\\\\implies\tt{2*AD^2=72}\\\\\\\implies\tt{AD^2=\dfrac{72}{2}}\\\\\\\implies\tt{AD^2=36}\\\\\\\implies\tt{AD=\pm 6.}\\\\\\\underline{\text{Possible value of AD = 6.}}\\\\\\\boxed{\boxed{\bold{Length\:of\:median=6\:units.}}}$