Question

The points $A$ $\left(2a,4a\right),B\left(2a,6a\right)$ and $C\left(2a+\sqrt{3}a,5a\right)$ (when a>0) are vertices of

• A. an obtuse angled triangle
• B. an equilateral triangle
• C. an isosceles obtuse angled triangle
• D. a right angled triangle

Answer 1

The correct option is B an equilateral triangle

$lengths:AB=2a$

$BC=\sqrt{{(2a+\sqrt{3a}-2a)}^2+{(5a-6a)}^2}$

$=\sqrt{{3a}^2+a^2}=2a$

$AC=\sqrt{{(2a+\sqrt{3a}-2a)}^2+{(5a-4a)}^2}$

$=\sqrt{{3a}^2+a^2}$

$=2a$

$\because AB=BC=AC=2a$

$\therefore \text{it is an equilateral triangle}.$