Question

If an equilateral triangle ABC, AD is a median. Prove that 3AC^2 = 4AD^2.​

Answer 1

Answer:

4A$D^{2}$=3A$B^{2}$ is  proved.

Step-by-step explanation:

From the above question, they have given :

An equilateral triangle ABC, AD is a median.

Here we need to prove that 3A$C^{2}$ = 4A$D^{2}$

Given AD⊥ BC

D=90˚

Proof:

    Since ABC is an equilateral triangle,

    AB=AC=BC

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal.

ABD is a right triangle.

According to Pythagoras theorem,

    AB2=A$D^{2}$ + B$D^{2}$

    BD=1/2BC

    A$B^{2}$ =A$D^{2}$ +(1/2BC)2

    A$B^{2}$ =A$D^{2}$ +(1/2AB)2           [∵BC=AB]

    A$B^{2}$ =A$D^{2}$ +1/4A$B^{2}$

    A$B^{2}$=(4A$D^{2}$ +AB2)/4

    4A$B^{2}$ =4A$D^{2}$ +AB2

    4A$D^{2}$ =4A$B^{2}$–A$B^{2}$

    4A$D^{2}$ =3A$B^{2}$

Hence proved.

For more related question : https://brainly.in/question/28467835

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