Question

8. The perimeter of equilateral triangle is 60 cm. The area is
103 root cm2
100root3 cm2
20root3 cm2
30 root3 cm2​

Answer 1

Given :

perimeter of equilateral triangle is 60 cm

To find :

it's area

Solution :

perimeter of an equilateral triangle = 60

3a = 60

a = 60/3

a = 20 cm

area of an equilateral triangle = √3/4 a² sq. units

= √3/4 x 20 x 20

= √3/4 x 400

= 100√3 cm²

=> it's area is 100√3 cm²

then the option 2 is correct

Answer 2

Answer:

Option (b) 100√3 cm² is right answer.

Step-by-step explanation:

We have given that,

• Perimeter = 60 cm

• So, Semi Perimeter = $\dfrac{60}{2}$ = 30 cm

Hence,the Length of each side will be :]

➸ $\\ \sf a + a + a = 60$

➸ $\\ \sf 3 a = 60$

➸ $\\ \sf a = \dfrac{60}{3}$

➸ $\purple{\sf a = 20 \: cm}$

• Now, we will find the area of equilateral triangle by given below formula :]

$\bigstar\:\:\boxed{\underline{\underline {\sf Area = \sqrt{s(s - a)(s - b)(s - c)}}}} \: \: \bigstar$

Now, putting the given values in above formula we get :

$: \implies\sf Area = \sqrt{30(30 - 20)(30 - 20)(30- 20)}$

$: \implies\sf Area = \sqrt{30 \times 10 \times 10 \times 10}$

$: \implies\sf Area = \sqrt{3 \times 10 \times 10 \times 10 \times 10}$

$: \implies\sf Area = 10 \times 10 \sqrt{3}$

$: \implies \underline{ \boxed{\sf Area = 100 \sqrt{3} \: cm^{2} }}$