Question

The perimeters of an equilateral triangle and a square are same The area of triangle : area of square is

• A. $1:1$
• B. $4:3\sqrt{3}$
• C. $4:3$
• D. $3:2$

Answer 1

The correct option is B $4:3\sqrt{3}$

Let side of equilateral triangle $=a$

then Perimeter of an equilateral triangle $=3a$

Let side of square $=x$

then Perimeter of square $=4x$

Perimeter of Equilateral Triangle = Perimeter of Square

$3a=4x$

$a=\frac{4}{3}x$

Area of Equilateral Triangle $=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}(\frac{4}{3}x{)}^2=\frac{4}{3\sqrt{3}}{x}^2$

Area of Square $=x^2$

$\frac{AreaofTriangle}{AreaofSquare}=\frac{\frac{4}{3\sqrt{3}}{x}^2}{x^2}=\frac{4}{3\sqrt{3}}=4:3\sqrt{3}$