Question

In an equilateral ∆ABC, if AD is perpendicular to BC, then prove:-
3AB²=4AD²

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Answer 1

Answer:

A ∆ ABC, in which sides are

AB=BC=AC=a units

and AD is perpendicular to BC,

In ∆ ADB ,

AB ^ 2 = AD ^ 2 + BD ^ 2 (by Pythagoras theorem)

a ^ 2 = AD ^ 2 + (a / 2) ^ 2 [BD = 1/2BC , since in an equilateral triangle altitude AD is perpendicular bisector of BC]

a ^ 2 - a ^ 2 / 4 = AD ^ 2;

=(4a^ 2 -a^ 2 )/4=AD^ 2;

=3a^ 2 /4=AD^ 2; 3AB ^ 2 / 4

= AD ^ 2; [AB = a];

3AB ^ 2 = 4AD ^ 2

[FIGURE IS IN THE ATTACHMENT]

Answer 2

Answer:

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Explanation:

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