Question

the perimeter of an equaleteral triangle is 60 cm .the area will be

Answer 1

Answer:

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The answer is 100$\sqrt{3}$$cm^{2}$

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Step-by-step explanation:

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Given ,

perimeter =60 cm

semi perimeter =  60 / 2  = 30 cm.

Therefore the length of each side.

a+a+a=60

⇒3a=60

⇒a=   60   / 3

⇒a=20

∴ Area =   $\sqrt{s(s-a)(s-b)(s-c)}$

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

​⇒ Area =  $\sqrt{30*10*10*10}$

​⇒ Area =   $\sqrt{ 3*10*10*10*10}$

​⇒ Area =10×10$\sqrt{3}$

​⇒ Area = 100$\sqrt{3}$ $cm^{2}$

 ∴ so, the answer is 100$\sqrt{3}$$cm^{2}$

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Answer 2

Answer:

Check out below for answer!

Step-by-step explanation:

Given  perimeter = 60 cm

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

                          =30 cm.

Therefore the length of each side =

a+a+a=60

⇒3a=60

⇒a =  $\frac{60}{3}$ (transposed)

⇒a=20

Hence, each side = 20cm

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

(s = Semi Perimeter

a = 1st side

b = 2nd side

c = 3rd side)

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

= $\sqrt{30*10*10*10}$

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

= 10 × 10$\sqrt{3}$

= 100$\sqrt{3}$ $cm^{2}$

Therefore,

      The area = $100\sqrt{3} cm^{2}$

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