Question

The perimeter of an equilateral triangle is $60$ cm, then the area is

• A. $10\sqrt{3}{\text{cm}}^2$
• B. $15\sqrt{3}{\text{cm}}^2$
• C. $20\sqrt{3}{\text{cm}}^2$
• D. $100\sqrt{3}{\text{cm}}^2$

Answer 1

The correct option is D $100\sqrt{3}{\text{cm}}^2$

Given

perimeter $=60$ cm

semi perimeter $=\frac{60}{2}=30$ cm.

Therefore the length of each side.

$a+a+a=60$

$\Rightarrow 3a=60$

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

$\Rightarrow a=20$

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

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

$\Rightarrow$ Area = $\sqrt{30\times 10\times 10\times 10}$

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

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

$\Rightarrow$ Area = $100\sqrt{3}c{m}^2$

$\therefore$ so, the answer is D. $100\sqrt{3}c{m}^2$