The equation of the base of an equilateral tr | vedclass

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(C) Let $p$ be the length of the perpendicular from the vertex $(2, -1)$ to the base $x + y - 2 = 0$.The formula for the perpendicular distance from a

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$\sqrt{2/3}$

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(C) Let $p$ be the length of the perpendicular from the vertex $(2, -1)$ to the base $x + y - 2 = 0$.The formula for the perpendicular distance from a point $(x_1, y_1)$ to the line $Ax + By + C = 0$ is $p = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Substituting the values,we get $p = \frac{|1(2) + 1(-1) - 2|}{\sqrt{1^2 + 1^2}} = \frac{|2 - 1 - 2|}{\sqrt{2}} = \frac{1}{\sqrt{2}}$.For an equilateral triangle with side length $a$,the altitude $p$ is given by $p = a \sin(60^{\circ}) = \frac{a\sqrt{3}}{2}$.Equating the two expressions for $p$: $\frac{1}{\sqrt{2}} = \frac{a\sqrt{3}}{2}$.Solving for $a$: $a = \frac{2}{\sqrt{2} 	imes \sqrt{3}} = \frac{\sqrt{2}}{\sqrt{3}} = \sqrt{\frac{2}{3}}$.

The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. The length of the side of the triangle is

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