Question

If $g\left(x\right)$ is defined on $[-1,1]$ and the area of the equilateral triangle with two of its vertices $(0,0)$ and $(x,g(x\left)\right)$ is $\frac{\sqrt{3}}{4}$, then

• A. $g\left(x\right)=\pm \sqrt{(1-x^2)}$
• B. $g\left(x\right)=-\sqrt{(1-x^2)}$
• C. $g\left(x\right)=\sqrt{(1-x^2)}$
• D. $g\left(x\right)=\sqrt{(1+x^2)}$

Answer 1

The correct option is A $g\left(x\right)=\pm \sqrt{(1-x^2)}$

Area of equilateral Triangle is $=\frac{\sqrt{3}}{4}(\text{side}{)}^2$

$=\frac{\sqrt{3}}{4}(x^2+(g\left(x\right){)}^2)=\frac{\sqrt{3}}{4}$

$\Rightarrow x^2+\left(g\right(x){)}^2=1$

$\Rightarrow g\left(x\right)=\pm \sqrt{1-x^2}$