Question

The area of a square is $64c{m}^2$. If the side of the square is equal to the side of an equilateral triangle, the find the area of the triangle .

• A.
  $16\sqrt{3}$
  
• B.
  $14\sqrt{3}$
• C.
  $9\sqrt{3}$
• D.
  $8\sqrt{3}$

Answer 1

The correct option is A

$16\sqrt{3}$

$\text{Area of square}=sid{e}^2\Rightarrow 64=sid{e}^2\Rightarrow Side=8cm\text{Side of triangle =8 cm}\text{Semi perimeter of the triangle s}=(8+8+8)/2cm=12cm\text{Area of the triangle}=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{12\left(4\right)\left(4\right)\left(4\right)}=\sqrt{768}=16\sqrt{3}cm$

So, option a is correct.