Question

Ar​ea of an equilateral t​riangle is 163cm.find perimeter

Answer 1

Area = ½bh

 

B = a/2, since this is an equilateral triangle.

 

And h can be expressed in terms of side of triangle, a, as

 

H^2 – a^2-(a/2)^2 = a^2-a^2/4 = 3a^2/4.

 

Therefore, h = ½*a*sqrt(3)

 

Therefore, 163 = ½ * ½ * a* ½ * a * sqrt 3

 

= 1/8 * a^2 * sqrt (3)

 

Or a^2 = 163*8/sqrt (3)

 

Or a^2 = 752.8648

 

Or a = sqrt (752.8648) = 27.44.

 

Therefore, perimeter is 3*27.44 = 82.32cm