Question

The perimeter of an equilateral triangle is $60cm$ then its area will be:

• A. $400\sqrt{3}sqcm$
• B. $100\sqrt{3}sqcm$
• C. $50\sqrt{3}sqcm$
• D. $200\sqrt{3}sqcm$

Answer 1

Answer: (B)

$100\sqrt{3}sqcm$

Given

perimeter $=60cm$

semi perimeter $=\frac{60}{2}$

$=30cm.$

Therefore the length of each side.

$a+a+a=60$

$\Rightarrow 3a=60$

$\Rightarrow a=\frac{60}{3}$

$\Rightarrow a=20$

Area $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{30(30-20)(30-20)(30-20)}$

$=\sqrt{3\times 10\times 10\times 10\times 10}$

$=100\sqrt{3}sq.cm$