The base of an equilateral triangle is along the line given by 3x+4y=9.

Question

The base of an equilateral triangle is along the line given by $3x+4y=9$. If a vertex of the triangle is $(1,2)$, then the length of a side of the triangle is:

Accepted Answer

Distance from $(1,2)$ to $3x+4y=9$: $\dfrac{|3+8-9|}5=\dfrac25$. This is the height of the equilateral triangle.

Height $h=\dfrac{\sqrt3}2a \implies a = \dfrac{2h}{\sqrt3} = \dfrac{2}{\sqrt3}\cdot\dfrac25 = \dfrac4{5\sqrt3}=\dfrac{4\sqrt3}{15}$

Solutions · 1