Question

the area of eqallaterlall triangles 81/3cm. what its height ​

Answer 1

Answer:

The area of an equilateral triangle = [a^2*3^0.5]/4 where a is the side.

So here we have [a^2*3^0.5]/4 = 81*3^0.5 (=140.2961154) , or

a^2 = 4*81 = 324, or

a = 18 cm

The height of the triangle = a sin 60 = 18 x sin 60 = 15.58845727 cm.

Answer: the height of the equilateral triangle whose area is 81*3^0.5 is 15.58845727 cm.

Check Area = bh/2 = 18 * 15.58845727/2 = 140.2961154 sq cm same as 81*3^0.5. Correct.

The height of the equilateral triangle whose area is 81*3^0.5 is 15.58845727 cm.