Question

Triangle DEF is an equilateral triangle.
seg DP perpendicular
side EF,
and E-P-F.
Prove that : DP×DP= 3 EP×EP
​

Answer 1

Step-by-step explanation:

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Answer 2

The expression is correct $DP^2=3EP^2$

Step-by-step explanation:

SINCE, the DEF is an equilateral triangle

∴ DE = EF = DF  .......eq(1)

NOW,

    ∵ The DP is perpendicular to EF.

    => The DP is bisecting the side EF.

∴ EP=PF

NOW,

        In ΔDEF we have ,

      =>    $DP^2+EP^2=DE^2$   (By pyhtagouros theorom)

      =>   $DP^2+EP^2=EF^2$    ( By using eq(1) )

      => $DP^2+EP^2=(2EP)^2$

           $DP^2+EP^2=4EP^2\\DP^2=3EP^2$

HENCE PROVED   $DP^2=3EP^2$