Question

The area of a square is $36c{m}^2$. If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.

• A. 18 cm
• B. 12 cm
• C. 15 cm
• D. 9 cm

Answer 1

The correct option is A

18 cm

Area of a square $={\text{Side}}^2$
$\Rightarrow 36={\text{Side}}^2$
$\Rightarrow \text{Side}=6cm$

Hence, side of triangle $=6cm$

Semi perimeter of the triangle, $s=\frac{6+6+6}{2}cm=9cm$
Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{9(9-6{)}^3}$
$=\sqrt{243}$
$=9\sqrt{3}c{m}^2$