Question

in an equilateral triangle ABC D is a point on side ​

Answer 1

Explanation:

given,

AB=BC.CA

BD=1/3BC

PROOF- BD=1/3 BC

IN ∆AEC

AC^2 =AE^2 + EC^2

(AC is a side of triangle

consider AC as (a) )

a^2 = AE^2 + (a/2)^2

AE^2 =a^2-(a)^2/2(taking LCM)

AE^2 = 4a^2/4-a^2/4

AE^2 = 3a^2/4

given BD=1/3BC

BD=a/3

DE=BE-DE

a/2-a/3=a/6=DE

IN∆ADE

AD^2=AE^2+DE^2

= 3a^2/4+(a/6)^2 (taking LCM)

=27a^2/36+a^2/36

28a^2/36 by cancelling

AD^2=7a^2/9

9AD^2=7AB^2

PROVED

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