You visited us 1 times! Enjoying our articles? Unlock Full Access!

Coordinates of a Point in Space

In the adjoin...

Question

In the adjoining figure, ${A B}^{2} + {A C}^{2} = 122$ and $B C = 10$ . Find the length of the median on side $B C$ .

Open in App

Solution

Given, $B C = 10$ and $A B^{2} + A C^{2} = 122$
Since, $B C = 10$ cm , $B Q = \frac{1}{2} B C = 5$ cm
By Apollonius theorem,
$A B^{2} + A C^{2} = 2 (A Q^{2} + B Q^{2})$
$122 = 2 (A Q^{2} + 5^{2})$
$A Q^{2} = 61 - 25$
$A Q = 6$ cm
Length of median = 6 cm

Suggest Corrections

Similar questions

In the given figure, {AB}^{2} + {AC}^{2} = 122 and BC = 10 . Find the length of the median on side BC .

△ A B C

A B^{2} + A C^{2} = 122

10

A Q

{A B}^{2} + {A C}^{2} = 122

B C = 10

A Q

△ A B C, {A B}^{2} + {B C}^{2} = 122, B C = 10

B C

In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

(i)

(ii)

(iii)

Join BYJU'S Learning Program