Question

8. Find the area of an equilateral triangle whose
perimeter is 36 cm. Also, find its height.
​

Answer 1

Perimeter= 36cm

Let each side be x.

So,

x+x+x=36

3x=36

x=36/3

x=12

Using herons formula

root under s(s-a)(s-b)(s-c)

=18(18-12)(18-12)(18-12)

=18×6×6×6

=36 root 3

Height=1/2*b*h=36 root 3

=6h=36 root 3

=h=6 root 3

Answer 2

Heya!!

We know that perimeter of equilateral triangles = 3a

So,

=>36 = 3a

=> a = 12

Hence, one side of equilateral triangles measures 12cm.

Now,

Area of triangle by apply Heron's formula we get :

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

Applying values as :

semi perimeter = 18 cm

And, values of a, b & c = 12cm

$= \sqrt{18(18 - 12)(18 - 12)(18 - 12} \\ = \sqrt{18 \times 6 \times 6 \times 6} \\ = \sqrt{6 \times 3 \times 6 \times 6 \times 6} \\ = 36 \sqrt{3} cm {}^{2}$

Now, we also know that area of triangle is

= 1 / 2 * base * height

So,

$36 \sqrt{3} = 12 \times \div 2 \times \: height \: \\ 36 \sqrt{3} \: = \: 6 \times \: height \: \\ height = \: 36 \sqrt{3} \div 6 \\ = 6 \sqrt{3} cm$

Hope it helps

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