The vertex of an equilateral triangle is (2, –1) and the equ... | MATH - PROBLEMS RELATED TO TRIANGLE | SolveeIt | Solveeit

Today, August 24

Question

The vertex of an equilateral triangle is (2, –1) and the equation of its base is x + 2y = 1. The length of its sides is :

A

$\frac{4}{\sqrt{15}}$

B

$\frac{2}{\sqrt{15}}$

C

$\frac{4}{3\sqrt{3}}$

D

$\frac{1}{\sqrt{5}}$

Answer

$\frac{2}{\sqrt{15}}$

Explanation

Solution

AD = $\frac{|2–2–1|}{\sqrt{5}}$

= $\frac{1}{\sqrt{5}}$

AB = AD cosec 60⁰

= $\frac{1}{\sqrt{5}}$ × $\frac{2}{\sqrt{3}}$

= $\frac{2}{\sqrt{15}}$