Question

If (0,0),(3,root3),(3,p) are vertices of an equilateral triangle, then value of p is:
a) - root3
b) root3
c) 3
d) -3

Answer 1

Therefore the answer is a)-(root 3)

Answer 2

Therefore  $p = \sqrt{3}$

Explanation:

Given A (0,0),B(0,$\sqrt{3}$),C(3,p) are the vertices of a equilateral triangle.

The distance between (0,0) and(0,$\sqrt{3}$) is

=$\sqrt{(0-3)^2+(0-\sqrt{3} )^2}$

$=\sqrt{12}$

The distance between (0,0) and (3,p) is

=$\sqrt{(0-3)^2+(0-p)^2}$

$=\sqrt{9+p^2}$

Since it is a equilateral triangle .Then all sides are equal.

Therefore ,

$\sqrt{9+p^2}=\sqrt{12}$

$\Leftrightarrow 9+p^2 = 12$

$\Leftrightarrow p^2 = 3$

$\Leftrightarrow p = \sqrt{3}$