Question

Prove that AC square= AD square+ 3 CD square

Answer 1

We will apply Pythagoras Theorem in order to work out with the given problem.

Given :- angle B is of 90°. AD is the median, since, D is the mid point.

To prove :- AC² = AD² + 3CD²

Proof :-

By Pythagoras Theorem, we have

AC² = AB² + BC²

and, AD² = AB² + BD²

Let's think in other way to workout!

BC can be written as 2CD, since D is the midpoint.

=> BC² = (2CD)²

=> BC² = 4CD²

So, AC² = AB² + BC²

=> AC² = AB² + 4CD²

Again, since D is the midpoint, BD = CD

=> BD² = CD²

=> AD² = AB² + CD²

=> AB² = AD² - CD²

So now,AC² = AB² + 4CD²
and AB² = AD² - CD²

put the value of AB² in the equation.

=> AC² = AD² - CD² + 4CD²

=> AC² = AD² + 3CD²


Hence Proved :)

Answer 2

here is ur answer mate hope it will help u