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In an equilateral triangle, prove that t...

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Text Solution

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`AD botBC therefore In DeltaABD,AB^(2) = AD^(2) + BD^(2)`
`rArr AB^(2) =AD^(2) +(BC^(2))/(4) or 4AB^(2)+ BC^(2)`
`rArr 3AB^(2) = 4AD^(2)`
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