Question

In ΔABC, AB²+AC²=50. The length of the median AD=3. So, BC = ...,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 4
(b) 24
(c) 8
(d) 16

Answer 1

in triangle ∆ABC , we have to use the theorem of Apolloneous.
we know that,
For AD to be the median, we have,
AB² + AC² = 2(AD² + BD²)
Given, AB² + AC² = 50
⇒ 50 = 2(3² + BD²)
⇒ 50 = 2 (9 + BD² )
⇒ 25 = 9 + BD²
⇒ BD² = 16
⇒ BD = 4
⇒ BC = 2BD = 8
∴ Option (c) is correct.

Answer 2

In ∆ABC ,

AD is a median .

BD = DC

BD = BC/2 ---( 1 )

AB² + AC² = 50 ---( 2 )

AD = 3 ---( 3 )

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By Apollonius Theorem :

The sum of the squares of two sides

of a triangle is equal to twice the

square on half the third side plus

twice the square on the median which

bisects the third side.
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In ∆ABC , AD is the median then

AB² + AC² = 2( BD² + AD² )

AB² + AC² = 2 [ ( BC/2 )² + AD² ]

50 = 2 [ BC²/4 + 3² ]

25 = BC²/4 + 9

16 = BC²/4

BC² = 64

BC = √64

BC = 8

Therefore ,

Option ( c ) is correct

I hope this helps you.

: )