Question

Is an equilateral triangle abc point d is the midpoint of side bc . Prove that 4ad square = 3bc square?

Answer 1

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Answer 2

4AD² = 3BC² if D is mid point of BC in   an equilateral triangle abc

Step-by-step explanation:

Given

ABC is an equilateral Triangle

D is mid point of BC

To be proved

4AD² = 3BC²

Comparing ΔABD  & ΔACD

AD = AD Common

AB = AC  ( all sides of equilateral triangle are equal)

BD = CD  = BC/2  as mid point of BC

=>  ΔABD  ≅ ΔACD

=> ∠ADB = ∠ACB

∠ADB + ∠ACB = 180°   ( straight line)

=> ∠ADB = ∠ACB = 90°

=> in Δ ADB

AB² = AD² + BD²

=> AD² = AB² - BD²

=> AD² = BC² - (BC/2)²

=>AD² = BC² - BC²/4

=> 4AD² = 4BC² - BC²

=> 4AD² = 3BC²

QED

Proved

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