Math, asked by gourabdutta6317, 1 year ago

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

Answers

Answered by vikram991
2

\huge{\bf{\underline{\red{Solution :}}}}

Given,

  • ΔABC is an Equilateral triangle .

To Prove :

  • 4 x (square of altitude ) = 3 x ( Square of one side ).

Proof :

Let the Side of Equilateral triangle be a

And , AD is an altitude of ΔABC .

∴BD = DC = \bold{\frac{BC}{2}} = \bold{\frac{a}{2}}

Now Applying Pythagoras Theorem in ΔABC :

\implies \bold{\sf{AB^{2} = AD^{2} + BD^{2} }}}

\implies \bold{\sf{ a^{2}  = AD^{2} + [ \frac{a}{2} ]^2}}

\implies \bold{\sf{AD^{2} = a^{2} - \frac{a^2}{4}}}

\implies \bold{\sf{AD^{2} = \frac{3a^2}{4}}}

\implies \bold{\sf{4AD^2  = 3a^2}}}

[ So here 4 times of square altitude = 3 times of square of one side ]

Hence Proved

\rule{200}2

Answered by Anonymous
1

plz refer to this attachment

Attachments:
Similar questions