Question

If the perimeter of a square and an equilateral triangle are equal, then find which of the following option is correct?

• A. Area of triangle = Area of square
• B. Area of triangle > Area of square
• C. Area of triangle < Area of square
• D. None of the above

Answer 1

Answer:

C. Area of triangle < Area of square

Given:

The perimeter of a square and a triangle is equal.

Formula:

Area of square = a²                    (a = side)              

Calculation:

Let perimeter of square and perimeter of the triangle be 12 unit

Side of triangle = $\frac{12}{3} = 4 unit$

⇒ Area of triangle = $\sqrt{\frac{3}{4}}\times{4}\times{4}$

= 6.928 sq unit

Side of the square = $\frac{12}{4} = 3 unit$

⇒ Area of square = $3\times{3}$

⇒ 9 sq unit

∴ Area of triangle < Area of square