Question

The triangle ABC is given. Let BC 20 in , AB 30 in and the length of the median from the vertex A is AD 25 in . The length of AB is:​

Answer 1

Answer:

23.4 is a answer

mediun AD =

$\sqrt{ \frac{2.{ab}^{2} + 2. {ac}^{2} - {bc}^{2} }{4} }$

put the all given values

AD = 25, BC = 20 AC= 30

AND you get

AB = 23.4

Answer 2

Given in $\triangle ABC$, BC = 20 inches , AC = 30 inches

Length of median AD = 25 inches

$\therefore$ BD = 10 inches

Using Apollonius Theorem,

$(AB^{2}+AC^{2})=2\times (BD^{2}+AD^{2})\\(AB^{2}+30^{2})=2\times (10^{2}+25^{2})\\AB^{2}+900=2(100+625)\\AB^{2}+900=1450\\AB^{2}=550\\\therefore AB=\sqrt{550} =23.45 inches$

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