Question

The equations $y=\pm \sqrt{3}x,y=1$ are the sides of

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

Answer 1

The correct option is A

an equilateral triangle

Step 1: Sides of the triangle.

The given equation is $y=\pm \sqrt{3}x,y=1$.

$$\begin{gathered} y=\sqrt{3}x.........\left(i\right) \\ y=-\sqrt{3}x.......\left(ii\right) \\ y=1...............\left(iii\right) \end{gathered}$$

On solving equations $\left(i\right)\&\left(ii\right)$, we get $x=0,y=0$.

So, $A=\left(0,0\right)$

Again, on solving equations $\left(ii\right)\&\left(iii\right)$.

$x=-\frac{1}{\sqrt{3}},y=1$

So, $B=\left(-\frac{1}{\sqrt{3}},1\right)$

Similarly, $C=\left(\frac{1}{\sqrt{3}},1\right)$

Step 2: Length of the sides of the triangle.

Using distance formula, $AB=BC=AC=\frac{2}{\sqrt{3}}$.

So, it is an equilateral triangle.

Hence, the given triangle is an equilateral triangle and therefore option $\left(A\right)$ is correct.