Question

If three points $(0,0),(3,45)$ and $(3,\lambda )$ form en equilateral triangle, then the value of $\lambda$, is _______.

• A. $96$
• B. $18$
• C. $50$
• D. None of the above values of $\lambda$ makes an equilateral triangle

Answer 1

The correct option is D None of the above values of $\lambda$ makes an equilateral triangle

given $A(0,0),B(3,45),C(3,\lambda )$ forms equilateral triangle

$\Rightarrow$ All lengths must be equal

$\therefore$ $\Rightarrow AB=AC$

$AB=\sqrt{2034}$,$AC=\sqrt{9+{\lambda }^2}$

$\therefore$ $\lambda =45$

$\Rightarrow$ There cannot be an equilateral triangle with these values