Question

seg ad is a median of triangle ABC if ab if AB= 12 AD= 10 AC is= 16 then find BC

Answer 1

Answer:20

In ∆ABC,

Seg AD is the median...(given)

.°.By apollonius theorem

AB²+AC²=2AD²+2BD²

.°.144+256=2×100+2BD²

400-200=2BD²

200/2=BD²

I.e. BD²=100

BD=10

BC=2BD

....(°.°D is the midpoint of seg BC)

BC=2×10

BC=20

Answer 2

In ∆ABC ,

AB = 12 , AC = 16 ,

median ( AD ) = 10 ,

BC = ?

By , Appolonius Theorem ,

2( BC² + AD² ) = AB² + AC²

=> BC² + 10² = ( 12² + 16² )/2

=> BC² + 100 = ( 144 + 256 )/2

=> BC² + 100 = 400/2

=> BC² = 200 - 100

=> BC² = 100

=> BC = 10