Question

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter, then:

• A. $X>Y$
• B. $X<Y$
• C. $X=Y$
• D. None of these

Answer 1

The correct option is B $X<Y$

Here the side of triangle will be $\frac{p}{3}$, side of the square will be $\frac{p}{4}$ where $p$ is the perimeter.
Area of triangle, $X=\frac{\sqrt{3}}{4}{\left(\frac{p}{3}\right)}^2=\frac{p^2\sqrt{2}}{36}=0.04p^2$
Area of Square, $Y={\left(\frac{p}{4}\right)}^2=\frac{p^2}{16}=0.0625p^2$
Therefore, $Y>X$