Question

find the perimeter n area of a equilateral triangle whose height is 12 cm ​

Answer 1

Let each side of the equilateral triangle be a cm.

Height of a equilateral triangle is the perpendicular bisector of the base

In the right angled triangle formed by the height and two sides,

${a}^{2} = {(\frac{ {a} }{2} )}^{2} + {12}^{2} \: \: \: \: \: \: |by \: pgt|$

${a}^{2} - \frac{ {a}^{2} }{4} = 144$

$\frac{ {3a}^{2} }{4} = 144$

${a}^{2} = 192$

$a = \sqrt{192} = 8 \sqrt{3}$

Now,

$perimeter = 3 \times 8 \sqrt{3} = 24 \sqrt{3}$

and,

$area = \frac{1}{2} \times 8 \sqrt{3} \times 12 = 48 \sqrt{3}$