Question

The perimeter of an equilateral triangle and a square are same then $\frac{areaof\Delta }{areof\square }=$

• A. $\frac{4}{3}$
• B. $1$
• C. $1.5$
• D. $<1$

Answer 1

The correct option is D $<1$

Let side of equilateral $△=a$

Side of square$=b$

Since, perimeter of triangle = perimeter of square

$\therefore 3a=4b\Rightarrow \frac{a}{b}=\frac{4}{3}$

$\therefore \frac{ar△}{ar△}=\frac{\frac{\sqrt{3}}{4}\times a^2}{b^2}=\frac{\sqrt{3}}{4}\times {\left(\frac{a}{b}\right)}^2=\frac{\sqrt{3}}{4}\times \frac{16}{9}=\frac{4}{3\sqrt{3}}<1$